Quadratic Function Problems Pdf

Search : Search : Quadratic Word Problems. Consider the quadratic function. I have a quadratic function problem that I've been trying to solve without success, the thing is is I know it's easy! Thanks for your answer! The only thing I'm having problems with now is understanding how to complete the square. Lesson 8 - Introduction to Quadratic Functions Mini-Lesson Page 278 Problem 2 MEDIA EXAMPLE – GRAPH QUADRATIC FUNCTIONS Given the Quadratic Function f(x) = x2 – 2x + 3, complete the table and generate a graph of the. Quadratic Equation Word Problems Worksheet How To Solve. Create a T separating the two ( ). The technique finds broad use in operations research and is occasionally of use in statistical work. Quadratic Equation Pdf Free Download Now: Quadratic Equation Question Pdf for Banking, SSC, RRB, FCI, Railway, UPSC, State PCS, Insurance & other Competitive exams. In some problems, we want the roots of the equation ax 2 + bx + c = 0 to lie in a given interval. When we plot these points and join them with a smooth curve, we obtain the quadratic graph shown above. + with lots of tips, answer keys, and detailed answer explanations for all of the problems. The length of a rectangle is 6 inches more than its. The graph of a quadratic function is a curve called a parabola. interpret solutions to real-life problems and explain which solutions are reasonable for the situation. quadratic and cubic functions. We did all our graphing using the calculator last year, so I didn't think it really mattered. the quadratic and sometimes the problem is merely asking to evaluate a quadratic function. We will open a new window containing your custom quadratic equations worksheet. Theshapeofthegraphoff(x) = ax2 +bx +c iscalledaparabola. Examples of functions - drdelmath. S D VA6lkl0 lrDi9g2hMtdsk SrweysxeFr7v4eLdP. For example, consider 6x^2 + 7x - 20 = 0. Quadratic Functions. pdf to word problems formatting Equation, that is, an equation involving a quadratic function. Write a quadratic function to model this situation. The equation above represents a quadratic function where a and b are constants. Problems: A good test on the use of quadratic equations in some real life situations. Practice Book. Graph the function. Performance Assessment Task Quadratic (2006) Grade 10 The task challenges a student to demonstrate an understanding of the graphical properties of a quadratic function given by its formula. Quadratic Word Problems Involving Maxima or Minima LSC‐O 5/2011 Page 1 of 4 Problem A Instructions. QUADRATIC EQUATIONS WORD PROBLEMS Professor Howard Sorkin - MAT 1033 - INTERMEDIATE ALGEBRA Sample Problems 1. Application of Quadratic Functions Worksheet. High school math students can use these algebra problems for study purposes. Look at example 1. com ©R n220s1z2u GKBustsab LShoCf8t3wja8rSeZ hLOLCC7. For the following equations find the vertex of the parabola algebraically by completing the square. Solve Word Problems Using Quadratic Equations Follow along with the PDF. draw a picture 2. Our quadratic equations calculator lets you find the roots of a quadratic equation. It is natural to regard these developments as preludes and assert that the alge- braic theory of quadratic forms properly begins with a seminal 1937 paper of E. 5 Calculate where the castle ditches have to be built by using the quadratic formula. Chapter 3 Quadratic Programming 3. Lecture 5 : Solving Equations, Completing the Square, Quadratic Formula An equation is a mathematical statement that two mathematical expressions are equal. Review Vertex and Discriminant of Quadratic Functions the graph of a quadratic function written in the form f(x) = a x 2 + b x + c has a vertex at the point (h , k) where h and k are given by. The standard form of quadratic equation is the equation in form of ax 2 + bx + c = 0. De nitions: Quadratic functions: y = f(x) = ax2 + bx+ c (a 6= 0) ; where a;b;c are real numbers. of a quadratic equation. 3: Solving Quadratic Equations by Completing the Square • Section 4. Students will need to decide which strategy to use, a table of values, graphing, or factoring, is best to determine the answer that is required. The course will be covered in Hindi. mathematicsvisionproject. We will look at four methods: solution by factorisation, solution by completing the square, solution. 1 Constrained quadratic programming problems A special case of the NLP arises when the objective functional f is quadratic and the constraints h;g are linear in x 2 lRn. Question: The main section of a certain bridge has cables in the shape of a parabola. "Today you will be investigating/experiencing the quadratic function from real data and interpreting the graph's x and y. PDF | In this paper the fractional Quadratic objective programming problem (QFPP) with linear constraints, has been defined and developed. Word Problems 17. Writing Quadratic Equations & Functions In Vertex & Standard Form, 3 Points, Table, Graph, Roots. The other answer was 2. Also known as motion problems, these problems ask you to describe motion. A quadratic equation takes the form ax2 +bx+c = 0 where a, b and c are numbers. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior. over solving quadratic non-convex programming problems. pdf: File Size: 1880 kb: File Type: pdf. Given two points on the graph of a linear function, we may find the slope of the line which is the function’s graph, and then use the point-slope form to write the equation of the line. I selected problems that relate to sports whenever possible because most teenagers can relate to sports. In this article, we concentrate exclusively on quadratic problems, that is, on problems whose twentieth-century solution involves setting up a quadratic equation in one unknown. Quadratic Functions 311 Vocabulary Match each term on the left with a definition on the right. solving quadratic equations as compared to other topics. Show pictures of real world parabolas. Chapter 6 Quadratic Functions and Inequalities285 Prerequisite Skills To be successful in this chapter, you’ll need to master these skills and be able to apply them in problem-solving situations. linear-quadratic or quadratic-quadratic equations is a solution of the system. Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years. "x" is the variable or unknown (we don't know it yet). Honors Algebra II Rev 07/08 1 Course description In Algebra II, students learn to represent various families of functions—linear, quadratic, exponential, logarithmic, radical, and rational—in various ways: as verbal descriptions, equations, tables, and graphs. You may select the numbers to be represented with digits or in words. Algebra Worksheets, Quizzes and Activities. Apply algebraic concepts using both real-world problems and "pure" math. The expression b2 - 4ac is called the discriminant and given the letter δ (delta). Write the given conditions as equations in a, b and c. Quadratic equations are also needed when studying lenses and curved mirrors. 15 years ago, she was twice as old. Such an NLP is called a Quadratic Programming (QP) problem. The following activities do NOT build upon each other. Graphing Quadratic Functions. The curve is called a parabola. Exponential Function Word Problems Exponential growth is modelled by y= y 0ekt There are four variables, the initial amount, y 0, the time t, the growth factor k, and the current amount y:You should be comfortable with nding any one of these four, given the other three. Partner Activity: Students work in pairs on a Tic-Tac-Toe activity to practice further. The general form of a quadratic polynomial is ax 2 +bx+c, where a, b, c are real numbers such that a is not equal to 0 and x is a real variable. Complete a table of values and graph =y x 2. Sample business change plan free printable homework sheets for teachers phd dissertation proposal examples in public health homework schedule template kids melaleuca business plan example interpretation essay an essay on the civil rights movement assignment the world 1994 pbs problem solving with ratio and proportion similar figures worksheet writing homework 2nd grade. Quadratic Equations When solving a quadratic equation of the form ax2 -+- c O by taking square roots, you may need to use the following properties of square roots to simplify the solutions. Algebra word problem worksheets for Algebra I and Algebra II courses. grand central - the creative station. The vertex in the third quadrant and two x-intercepts d. 2 Find the gradient of a graph. This paper proposes the combination of a net cash flow based quadratic loss function and componentwise L 2 Boosting as suitable method to estimate public market trading strategies that replicate private equity fund cash flows. Systems of Linear and Quadratic Equations HSA-REI. Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4). Class Notes. Word Problems involving Quadratic Equations Height in feet Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART. Comparing Graphs - Students are given an hourly rate of pay and infer coordinates for (h, $) over a range of hours. A quadratic equation, or second degree equation, is an algebraic equation of the form: ax2 + bx + c = 0,. Quadratic Equations mc-TY-quadeqns-1 This unit is about the solution of quadratic equations. x2 −x = 9 x2 −1x = 9 To complete the square:. Solve the Quadratic Equations by Factoring Worksheet # 2 1. A ball is tossed in the air from a height of 5 feet and the following data is recorded. Unit 8 – Quadratic Functions and Their Algebra. Free 25 printable worksheet on using the quadratic formula-this sheet focuses on real solutions. Our quadratic equations calculator lets you find the roots of a quadratic equation. 7 ­ Quadratic Functions & Transformations Mr. Quadratic Function Notes Page # 1 Algebra Notes: Quadratic Functions Polynomials Equations. 1 Use the the technique of ‘completing the square’ to solve each of the following equations. Quadratic equations are also used in other situations such as avalanche control, setting the best ticket prices for concerts, designing roller coasters, and planning gardens. Solve quadratic function word problems by determining each term of the quadratic equation and then solving for x when the equation is equal to zero. Duration: 0 hrs 50 mins Checkup: Lessons Learned. Quadratic Functions, Optimization, and Quadratic Forms Robert M. Writing Quad/eq. Application Problems For Cubic Functions. Whitt: Solving Quadratic Equations by Completing the Square Worksheet - Applications of Quadratic Functions ( Answer Key ). Next Chapter: QUADRATIC EQUATIONS. The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation. Linear functions. The pad on which the facility is set up measures 20 feet by 30 feet. You can start with any form but for this example we will start with vertex form. The initial velocity (launch speed) was 19. Problems to work out together in class. Kinematics (Description of Motion) Problems. 1-based loss function such that exact recovery and quadratic convergence of the proposed scheme are guaranteed. Function notation. 5: Discriminant Nature of the Roots. 54 seconds which is when the ball reached the ground (x-axis). Neglecting air resistance, the height h is feet of the object above ground after t seconds is given by the quadratic. Babe Ruth, a baseball player, hits a “major league pop-up” so that the height of the ball, in metres, is modeled by the function h t t( ) 5( 3) 46 2, where t is time in seconds. The special case for this problem was solved by using the. Description. 5 Explain, using examples, why the graph of a quadratic function may have zero, one or two x-intercepts. It also means that our output variable Functions within functions, dreams within dreams. These take the formax2+bx+c =0. Write the quadratic function f(x) = (3 − x)2 in standard form. quadratic function problems :'( Kindly help me about this quadratic equation please. com Mobile: 9999 249717. t Z cAplpld cr3i rg lhxt Hs6 wrheps ae Nrhv Yetd n. The other answer was 2. How long would it take a water balloon dropped from the treehouse to fall to the ground? A) 1. Kevin Regardie. Also Eample: The graph of a quadratic function has a ver distinct. Solve Word Problems Using Quadratic Equations Follow along with the PDF. Examples of Functions. Examples (a) y x2 2x 3 is a quadratic function of x. The initial velocity (launch speed) was 19. Lesson Previews. A study by Clarkson (1991) found that comprehension errors make up a high proportion of the errors made when students attempt to solve mathematical word problems. : Factoring; Completing the Square. Quadratic Programming A linearly constrained optimization problem with a quadratic objective function is called a quadratic program (QP). ” SIAM Journal on Optimization. ) Courtney is building a rectangular wading pool. Mathematics: Roots of Polynomials: An Introduction Contents 1. Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4). Modeling a Quadratic Function Using Various Word Problems Example 2: Complete each word problem using techniques learned in previous concepts. Year 10 maths Here is a list of all of the maths skills students learn in year 10! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. The steps for solving word problems involving quadratic equations are the same as for solving word problems involving linear equations. Find the time in which each tap can separately fill the tank. pdf word problems Solve these simultaneous equations and check that the answer is the same as. So after 4. This Long Division Worksheet the number of digits for the divisors and quotients may be varied from 1 to 3. Quadratic expressions that are equal to zero are called quadratic equations. Quadratic Functions Problems. For example, the point (2, 4) is a solution of the system y = x + 2 y = x2 The coordinates x = 2 and y = 4 satisfy both equations. These take the form ax2+bx+c = 0. I can use the discriminant to determine the number and type of solutions/zeros. These Algebra 1 Equations Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. A quadratic equation in one variable is any equation Documents. Word Problems 17. Quadratic Equations. : To solve quadratic equations by factoring and to understand what the solutions represent in a problem situation. The graph of the function is a. Comparing Graphs - Students are given an hourly rate of pay and infer coordinates for (h, $) over a range of hours. Quadratic functions frequently appears when solving a variety of problems. g(x) = 2x3 + 10x − 3x represents a quadratic function. ) 3x2 Quadratic-By-Factoring. NaN Quadratic Function (Quadratic equation) is the most advanced application for solving quadratic function problems. quadratic word problems projectile motion If you missed the flip chart, you can copy the notes by viewing the PDF version. How to derive and solve equations from worded quadratic problems. x 2 - 12x + 9 = y x 2 + 9x + 7 = y 2x 2 + 8x - 20= y. Algebra Topics Integers Rational Numbers Real Numbers Absolute Value Algebraic Expressions Equations Polynomials Monomials Linear Equations. See our to reinforce your knowledge of Equations. 14 M, and do the same reaction at the same temperature so that that K c. Key words: Quadratic Programming, Optimization, Active Constraints. Share on Facebook. Solve 2x2 32 A glimpse into what researchers say: Students’ difficulties with the quadratic equations might be because:. Quadratic Equations - Part II; Quadratic Equations : A Summary; Applications of Quadratic Equations; Equations Reducible to Quadratic in Form; Equations with Radicals; Linear Inequalities; Polynomial Inequalities; Rational Inequalities; Absolute Value Equations; Absolute Value Inequalities; Graphing and Functions. Kevin Regardie. Visit Mathway on the web. Determine which graph is the steepest without using a graphing calculator and without graphing. Halve the coefficient of x (which here is 2) and add to x in a bracket squared. Class Notes. Solve quadratic equations by graphing. The reason of the occurrence of the errors is because students have difficulty in solving quadratic equations. Candidates those who are preparing for Bank PO/Clerk and all other competitive Exams can also download this in PDF. 17 - Quadratic Function. Quadratic equations 1 – Math puzzle I’ve included three different sizes of the same puzzle. Solve quadratic function word problems by determining each term of the quadratic equation and then solving for x when the equation is equal to zero. Economists can model revenue and profit functions with quadratic equations. Solve Word Problems Using Quadratic Equations Follow along with the PDF. Modeling a Quadratic Function Using Various Word Problems Example 2: Complete each word problem using techniques learned in previous concepts. Example: A radiation control point is set up near a solid waste disposal facility. Projectile Problems. All quadratic equations have two roots/solutions. Problem solving subtraction grade 2. The complete contents of this algebra textbook are available here online. In this Module learners explore and analyse the characteristics of the quadratic function y = ax2 + bx + c and the effect of the parameters a, b and c on the behaviour of the function and form of the graph of the function. Plot the points and connect them with a smooth cu rve to form a parabola. This paper explores the mathematics behind optimal portfolio construction when relative utility and risk are considered together in a general sense. A parabola is an equation of the form y = a x 2 + bx + c. ©6 xKruht1aG 4SVoDfet1wyaOrceZ GLPLXCZ. The most general parabola, shown at the right, has the equation y = x 2. QUADRATIC FUNCTIONS word problems 1 The value of Jenifer’s stock portfolio is given by the function R( P) = − 3 P² + 73 P+ 50 , where R( P) is the value of the portfolio in hundred of dollars. Solving Quadratic Equations: Solving by Factoring Solving Quadratic Equations by Factoring Completing the Square: Completing the Square: Solving Quadratic Equations Completing the Square Quadratic Formula: Solving Quadratic Equations: Solving with the Quadratic Formula Solving Quadratics-The Quadratic Formula Problem Solving: Word Problem. Recall that a quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0, where a ≠ 0. Right from inequalities worksheet, pdf to point, we have got everything included. The technique finds broad use in operations research and is occasionally of use in statistical work. SOLVING QUADRATIC EQUATIONS A quadratic equation in is an equation that may be written in the standard quadratic form if. 6 m/s, and the coefficient on the linear term was "19. A polynomial of degree 2 is called a quadratic polynomial. superprof resources. An object that rises. Understanding quadratic functions is an important skill that goes beyond the classroom doors. For each function, a) determine if it opens up or down, b) find the axis of symmetry, c) find the vertex, d) find the y - intercept, e) graph the function, f) determine if it has a maximum or minimum and what that value is, and g) identify the domain and range. Plan your 60-minute lesson in quadratic functions or Math with helpful tips from Rhonda Leichliter. pdf 27 Solving System of Equations_Elimination Method_. Exercise 4. Quadratic Functions. Quadratic Programming (QP) Problems. Quadratic Equations This unit is about the solution of quadratic equations. They produce a table and a graph of. Distinct. The thing that sets a quadratic apart is that the degree (the highest power of x) is 2. Worksheets For Teachers PDF Using Known Multiplication Facts Worksheets 6th Grade Math Pages Printable Frog And Toad All Year Comprehension Questions. Their study in Year 10 gives an excellent introduction to important ideas. 1 Maximize a Concave Objective Function, Minimize a Convex Objective Function. 5 Explain, using examples, why the graph of a quadratic function may have zero, one or two x-intercepts. x = −b± √ b2 −4ac 2a √. We will look at four methods: solution by factorisation, solution by completing the square, solution. Economists can model revenue and profit functions with quadratic equations. Listed below are word lessons that focus on giving students instruction on how to solve most types of word problems commonly found in algebra, geometry, and trigonometry. Graphing Quadratic Functions. Download: PDF. Lesson 8 - Introduction to Quadratic Functions Mini-Lesson Page 278 Problem 2 MEDIA EXAMPLE - GRAPH QUADRATIC FUNCTIONS Given the Quadratic Function f(x) = x2 - 2x + 3, complete the table and generate a graph of the function. I'm sure it's. Compare the coefficients in the equation to the standard form, ax^2 + bx + c = 0. Quadratic Equation Word Problems Worksheet How To Solve. let us discuss this problem here. Also known as motion problems, these problems ask you to describe motion. 8-meter tall platform. The Graph of a Quadratic Function * Shape: parabola, symmetric When a > 0 When a < 0 * Vertex:. Recent negative results in very high dimension, though (Blekherman) Isn’t it a very special formulation? No, we can approximate any semialgebraic problem!. To solve application problems involving quadratic functions. The discussion of function characteristics includes further development of the. These shapes are called conic sections and are the curves that you obtain if you take a slice through a cone at various different angles. solving quadratic equations as compared to other topics. To find the values of x1 and x2, factor f(x) if it is. equations from worded quadratic. The process dynamics are included only in the. More importantly, though, it forms the basis of several general nonlinear programming algorithms. Solve Quadratic Equations - Quadratic Formula and Factoring. pdf to word problems formatting Equation, that is, an equation involving a quadratic function. 4 1 = y x 4. 7 Complete the Square Video View: This video is more examples on completing the square; it also reviews graphing in vertex form. You may also come across construction type problems that deal with area or geometry problems that deal with right triangles. Solve quadratic equations by factoring Example: x2 + 5x + 6 = 0 (x + 3)(x + 2) = 0 Factoring x + 3 = 0 or x + 2 = 0 Apply zero product property x = -2 or x = -3 Solve two first degree equations. Algebra has no applications in the real world. Quadratic functions make good models for data sets where the data either increases, levels off, and then decreases, levels off, and then increases. It's long, but it covers about every special I use this sort of problem in my college classes to have an example for all the different nuances of quadratic function modelling - word problems. Since y = mx + b is an equation of degree one, the quadratic function, y = ax2 + bx + c represents the next level of algebraic complexity. I can identify a function as quadratic given a table, equation, or graph. 1 Constrained quadratic programming problems A special case of the NLP arises when the objective functional f is quadratic and the constraints h;g are linear in x 2 lRn. When we plot these points and join them with a smooth curve, we obtain the quadratic graph shown above. O Y aMXa7dtei LwRi8tdh0 nIWn2fAiinlivt5ey oAxlQg1eAbWrtaa C2V. QUADRATIC WORD PROBLEMS General Strategies • Read the problem entirely. 6 Solve an application which results in an exponential function. Find the time in which each tap can separately fill the tank. Create a T separating the two ( ). Follow the above steps to find the vertex and axis of symmetry. Created Date: 2/5/2013 10:11:49 AM. The value of a share of R. The x-intercepts of the graph of a quadratic function are the solutions to the related quadratic equation. 7 Complete the Square Video View: This video is more examples on completing the square; it also reviews graphing in vertex form. These quadratic function worksheets require Algebra students to evaluate the quadratic functions, write the quadratic function in different form, complete function tables, identify the vertex and intercepts based on formulae, identify the various properties of quadratic function and much more. Free Mathematics Tutorials, Problems and Worksheets. For example, consider the problem of approximately solving. (2018) Quadratic Support Functions in Quadratic Bilevel Problems. Linear Equations in 2 variables (Straight Lines) 6. Solve quadratic function word problems by determining each term of the quadratic equation and then solving for x when the equation is equal to zero. Unit 3: Quadratic Functions and Equations NC Objectives Covered: 1. 1 Graphing Quadratic Functions 249 Graphing Quadratic Functions GRAPHING A QUADRATIC FUNCTION A has the form y = ax2 + bx + c where a ≠ 0. High schoolers learn how different parameters affect the graph of a quadratic function. Substitute the given information into the equation. Solve the problem using Galileoʹs formula, d = 16t2. Solving Equations Worksheets Solving Linear Equations Worksheets PDF from Solving Equations Worksheets , source: pinterest. In mathematics, a quadratic function is a polynomial function of the form. PDF Doc xls RTF txt ppt. Check Your Understanding LESSON 29-1 PRACTICE 15. For example, consider 6x^2 + 7x - 20 = 0. Comparing Graphs - Students are given an hourly rate of pay and infer coordinates for (h, $) over a range of hours. Quadratic Word Problems Maxima and minima problems in algebra are solved using. Please keep it with your homework for any homework checks. Vocabulary and notation are very important to understanding and communicating in mathematics. So that you can easily get the logic of question. QUADRATIC EQUATIONS WORD PROBLEMS Professor Howard Sorkin - MAT 1033 - INTERMEDIATE ALGEBRA Sample Problems 1. And solve the linear equation. 10 23 quadratic word problems pdf name solving algebra writing addition and subtraction expressions convert math formula from pdf to word math plane quadratics overview and notes 10 23 Quadratic Word Problems Pdf Name Solving Algebra Writing Addition And Subtraction Expressions Convert Math Formula From Pdf To Word Math Plane Quadratics Overview And Notes Math Quadratic Equations Worksheet…. A quadratic equation is any equation/function with a degree of 2 that can be written in the form y = a x 2 + b x + c, where a, b, and c are real numbers, and a does not equal 0. Worksheet Solving Quadratic Inequalities and Quadratic Word Problems. Chapter 3 Quadratic Programming 3. Quadratic)Formula) 1. x = −b± √ b2 −4ac 2a √. Real Life Quadratic Equations Word Problems With Solutions Pdf. From the graph of the function f(x) = x², graph the following translations:. Since y = mx + b is an equation of degree one, the quadratic function, y = ax2 + bx + c represents the next level of algebraic complexity. 4: The Quadratic Formula • Section 4. In this Module learners explore and analyse the characteristics of the quadratic function y = ax2 + bx + c and the effect of the parameters a, b and c on the behaviour of the function and form of the graph of the function. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x -axis, or above the x -axis. A quadratic equation takes the form ax2 +bx+c = 0 where a, b and c are numbers. Word Problems involving Quadratic Equations Height in feet Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART. For the following equations find the vertex of the parabola algebraically by completing the square. interpret solutions to real-life problems and explain which solutions are reasonable for the situation. Let's start with a number problem. MrsC Ripponmath. On this page you can read or download gina wilson unit 8 quadratic equations homework 2 answers in PDF format. Our quadratic equations calculator lets you find the roots of a quadratic equation. Quadratic Equations - Part II; Quadratic Equations : A Summary; Applications of Quadratic Equations; Equations Reducible to Quadratic in Form; Equations with Radicals; Linear Inequalities; Polynomial Inequalities; Rational Inequalities; Absolute Value Equations; Absolute Value Inequalities; Graphing and Functions. Find when the equation has a maximum (or minumum) value. NN) [1] is one of the tools to solve combinatorial optimization problems. Right? Hopefully not. Now a definition of the linear and the quadratic equation with one unknown can be introduced.