17 Quadratic Functions
MEP Y9 Practice Book B. 205. 17.3 Quadratic Equations: Completing the Square Give your answers to 2 decimal places. (a). (b). (c). (d). (e). (f). (g). (h) x x.
Quadratic Functions
18 Feb 2013 13 Quadratic Functions. To answer this question remember that the equation of a parabola is a formula which describes the relationship ...
QUADRATIC EQUATIONS
Question 25 (***). A quadratic curve has equation. 2. y x bx c. = + + where a and b are Solve the following quadratic in x
QUADRATIC FUNCTIONS
quadratic function is often used to solve optimization problems. EXAMPLE Solution: What we are dealing with here is a quadratic function f(x)=0.2x. 2.
Quadratics
Find the function g for the translated graph giving your answer in the form g The quadratic function f is defined by f (x) = 3x2 – 12x + 11. (a) Write f ...
Functions and Their Graphs Jackie Nicholas Janet Hunter Jacqui
The quadratic polynomial equation Q(x) = ax2 + bx + c = 0 has two roots that Use the graph to answer the following questions. a. State the roots of f(x) ...
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For a griddable question determine the best answer to the question. Then fill in the answer on your answer document. 1 The graph of quadratic function r is
POLYNOMIAL EXAM QUESTIONS
Question 55 (****). The quadratic function f is given in terms of three non zero constants a
Quadratic Equations
The number a cannot be zero. In this unit we will look at how to solve quadratic equations using four methods: • solution by factorisation. • solution by
THE QUADRATIC FUNCTION
Quadratic functions frequently appears when solving a variety of problems. ANSWERS TO EXERCISES. EXERCISE 1 a y = (x + 3)2 b. 0. –3. 9 y = (x + 3)2 x y.
Quadratic Equations and Functions
8.3 Equations in Quadratic Form. 8.4 Graphs of Quadratic Functions Note: The solution may also be written as ... Practice Problems. • e-Professors.
17 Quadratic Functions
x = 4. Note that in this example the equation has only one solution. Example 4. Solve the following equations: (a). 2. 3.
QUADRATIC FUNCTIONS
The meaning of the vertex as the maximum or minimum point for the quadratic function
Quadratic Functions
Feb 18 2013 This topic introduces quadratic functions
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10-5 Factoring Using the Distributive Property. 164. Chapter 10 Practice Test. 166. Answers and Explanations. 168. Chapter 11: Quadratic Functions.
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best answer to the question from the four answer choices provided. For a 7 Two characteristics of quadratic function p are given.
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Written-response Question 1 Sample Solution . A restriction on the domain of the graph of the quadratic function f(x) = a(x – c)2 + d that.
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POLYNOMIAL. EXAM. QUESTIONS f x as a product of a linear factor and a quadratic factor. ... A cubic function is defined in terms of the constant k as.
POLYNOMIAL EXAM QUESTIONS
POLYNOMIAL. EXAM. QUESTIONS f x as a product of a linear factor and a quadratic factor. ... A cubic function is defined in terms of the constant k as.
2.5 QUADRATIC FUNCTIONS PARABOLAS
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CHAPTER 13: QUADRATIC EQUATIONS AND APPLICATIONS
quadratic equation is a polynomial equation of the form Whereis called the leading term (or constantterm) Additionallyis call the +linear term +=and is called the constant coefficient SECTION 13 1: THE SQUARE ROOT PROPERTY SOLVE BASIC QUADRATIC EQUATIONS USING SQUAREROOT PROPERTY Squareroot? property LetandThen
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Quadratic Function Worksheets - Math Worksheets 4 Kids
Section 4: Solve the Quadratic Equations Solve the quadratic equations 1 x2– 3 = 45 (sq roots)2 4x2– 25 = 0 (sq roots) 3 2x2– 12x = 2x + 60 (factor/ZPP) 4 2x2– 5x – 12 (factor/ZPP) 5 x2+ 14x = 3 (complete the square)6 x2– 4x + 1 = 0 (complete the square) 7
QUADRATIC FUNCTIONS PARABOLAS AND PROBLEM SOLVING
2 5 Quadratic Functions Parabolas and Problem Solving 101 cEXAMPLE 4Minimizing areaFind the dimensions (xandh)for therectangle with the maximum area that can be inscribed in the isosceles triangleABCin Figure 28a Strategy: GraphKand?nd the highest point onthe graph (the vertex) Solution Follow the strategy
UNIT QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS
Free Response Questions 20 A quadratic function has a turning point at 38 Selected values for the function are shown in the table below (a) Finish filling out the table (b) State the zeroes of the function 21 For the quadratic function f xx x 2 41 defined on the interval 62 x
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The general form for a quadratic function is y = ax2 + bx + c Thus a = 4 b = –21 and c = –18 Defining Quadratic Equations: Standard Form with Real Numbers (02:50) By examining “a” in f (x)= ax2 + bx + c it can be determined whether the function has a maximum value (opens up) or a minimum value (opens down)
How do you find a quadratic function?
- Plug the x-values in f (x), obtain the y-values, and complete the function tables. Write a quadratic function based on the vertex (h, k) and a point (x, y) provided. Use the vertex form f (x) = a (x - h) 2 + k to find the quadratic function in this series of pdf worksheets.
How do you graph a quadratic function?
- The graph of a quadratic function is a parabola. The general form of a quadratic function is f ( x) = a x 2 + b x + c where a, b, and c are real numbers and a ? 0. The standard form of a quadratic function is f ( x) = a ( x ? h) 2 + k.
What is a quadratic function?
- A quadratic function is a mathematical function that describes a parabola. It is usually denoted by the equation y = ax^2 + bx + c, where a, b, and c are real numbers and x is a variable. -What is the domain and range of a quadratic function?
What is the standard form of a quadratic function?
- The standard form of a quadratic function presents the function in the form where (h, k) is the vertex. Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. As with the general form, if a > 0, the parabola opens upward and the vertex is a minimum.
Vertex Intercept Standard 2
y=(x-2) 2Vertex Intercept Standard 3
y=-x 2 -6x+4 Vertex Intercept Standard 4 y = -3(x - 1)(x - 5) Vertex Intercept Standard3. Solve the function graphically. y = x2 - 4x - 5 Vertex: _______ Solutions: ________ 4. Solve the function graphically. y = 2 (x + 1) (x - 3) Vertex: _______ Solutions: ________
2Section 1: Factoring Factor Completely! 1. x2 - 9x + 8 2. 3x2 - 48 3. 16x2 + 81 4. 100p2 - 49p 5. j2 - 10j + 21 6. 12x2 - 17x - 5 7. 24x2 - 14x - 5 8. 9x2 - 48x + 64
3Section 2: Graph the Quadratic Equations
1. y = -(x + 3)2 + 4 2. y = x2 - 2x - 3 Vertex: _________________ Vertex: _________________ x - Intercepts: ____________ x - Intercepts: ____________ Axis of Symmetry: ________ Axis of Symmetry: _________ Y-intercept: ______________ Y-intercept: _______________ Domain: _____________________ Domain: _____________________ Range: _______________________ Range: _______________________ Increasing: ____________________ Increasing: ____________________ Decreasing: ___________________ Decreasing: ___________________ Maximum Value of function: _____ Maximum Value of function: _____ Minimum Value of function: _____ Minimum Value of function: _____ Solutions: ______________________ Solutions: ______________________
43. y = -2x2 + 8 4. y = (x + 6) (x - 2) Vertex: _________________ Vertex: _________________ x - Intercepts: ____________ x - Intercepts: ____________ Axis of Symmetry: ________ Axis of Symmetry: _________ Y-intercept: ______________ Y-intercept: _______________ Domain: _____________________ Domain: _____________________ Range: _______________________ Range: _______________________ Increasing: ____________________ Increasing: ____________________ Decreasing: ___________________ Decreasing: ___________________ Maximum Value of function: _____ Maximum Value of function: _____ Minimum Value of function: _____ Minimum Value of function: _____ Solutions: ______________________ Solutions: ______________________
5 Simplify. Section 3: Exponents and Radicals 1. 5a 3 ⋅3a 10 2. -7x 3 2 3. 16x 5 y 2 6x 5 y 9 4. -2(evrthngisawsom) 0 5. 10x -2 6. 5 2x -3 7. x 1 5 i x 2 3 8. x 4 x 3 2Convert and evaluate. 9.
493 2 10. 125
-1 2
Simplify. 11.
-48 12. 27-53 13. 100x
16 y 17 14. 16 2 6 15.
528+37
16. 4+2 7-35 17. 3 5 18. 1-6 2+6Simplify. 19.
4-27 20. -25--49 21.28x
5 y 20
22. (5 - i) - (-1 + 2i) + 6i 23. -3(5 - 4i) 24. (2 + 10i) (2 - 10i) Rationalize the denominator. 25.
3 6-2i 26.2i-4 5+i 7
Section 4: Solve the Quadratic Equations Solve the quadratic equations. 1. x2 - 3 = 45 (sq. roots) 2. 4x2 - 25 = 0 (sq. roots) 3. 2x2 - 12x = 2x + 60 (factor/ZPP) 4. 2x2 - 5x - 12 (factor/ZPP) 5. x2 + 14x = 3 (complete the square) 6. x2 - 4x + 1 = 0 (complete the square) 7. x2 + 2x + 8 = 0 (Quadratic Formula) 8. 2x2 - 4x = 30 (Quadratic Formula)
8Solve the quadratic equations (choose a method) 9. x2 - 11x + 18 = 0 10. 2(x + 3)2 + 10 = 50 11. 3x2 + x = 3 12. 4x2 + 25 = 0 13. 9x2 + 36x = 0 14. x2 + 20x + 104 = 0 15. 18x2 + 12x + 2 = 0 16. x2 + 17x + 200 = 13x - 43
9Section 5: Systems 1. A system of equations is: ________________________________________________ 2. The solution(s) to a system is: ____________________________________________ Solve each system by graphing. If there is a solution, write it!! If the equations share infinite solutions, say so!! If they share no solutions, write No Solution. Check your work!!!! 3. y = -(x + 4)2 - 1 y = 3|x+4| - 5 4. x + y = 4 y = -(x + 5)2 Solution: ___________________ Solution: ___________________ Use substitution to find the solutions to the systems. Then CHECK with a calculator!! 5. y = x2 - 7x + 4 y = x - 3 6. y = x2 - 5x + 10 y = 2x2 - 6x + 4
107. Which of the following are quadratic functions? (Circle all that apply) (a)
fx 1 x 2 +6x-2 (b) fx =2x 2 +1 (c) f(x) = 5 - 3x (d) fx =-(x+3) 2 -8 (e) fx =-x-4 (f)8. Find the discriminant and determine the number and type of solutions. y = 3x2 - 18x + 8 Discriminant: ________________ Number and Type of Solutions: ______________________ Convert to standard form (by multiplying). 9. y = (x + 4) (x - 3) 10. y = 2 (3x + 5) (x - 2)
Convert to intercept form (by factoring).
11. y = x2 - 16x + 64 12. y = 2x2 - 3x - 20
Convert to vertex form (complete the square - refer to page 42 and 43). 13. y = x2 + 12x - 3 14. y = 2x2 - 20x + 1
11QUESTION ANSWER A ANSWER B 1 What is the form of the function: y = 2x2 + 3x + 2 Intercept Form Standard Form 2 What is the form of the function: y = 2(x + 3)2 - 10 Vertex Form Intercept Form 3 What is the form of the function: y = - (x + 3) (x - 8) Intercept Form Standard Form 4 What formula will find the x-coordinate of the vertex for standard form?
x= -b 2a x= b 2 25 What formula will find the x-coordinate of the vertex for intercept form?
x= p-q 2 x= p+q 26 What is the value of C that would complete the square: x2 - 4x + C 4 16 7 What is the a-value: y = 2x2 + 5x + 2 1 2 8 What type of polynomial is always prime? A binomial sum of squares A trinomial 9 What method would you use to solve the equation: y = (x + 3) (2x + 1) Zero Product Property Complete the Square 10 What method would you use to solve the equation: y = 4x2 + 10 Square Roots Method Quadratic Formula 11 What method would you use to solve the equation: y = x2 + 10x + 3 Square Roots Method Complete the Square 12 The discriminant is 24. How many and what type of solutions are there ? 2 Real 1 Real 13 The discriminant is -10. How many and what type of solutions are there ? 2 Imaginary 2 Real 14 The discriminant is 0. How many and what type of solutions are there ? 1 Real 2 Real 15 What calculator function can you use to find the vertex of a parabola? 2nd Graph 2nd Calc 16 How do you find any x-intercept? Substitute 0 for x Substitute 0 for y 17 How do you find any y-intercept? Substitute 0 for x Substitute 0 for y 18 What is the quadratic formula?
x= -bb 2 -4ac 2a x= -b±b 2 -4ac 2a Find the y-intercept of each function: 19. y = 2x3 + 5x - 3 20. y = 3 (x + 5) (2x - 1)quotesdbs_dbs14.pdfusesText_20[PDF] quadratic linear systems multiple choice
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