Module 2 Quadratic Functions Algebra 2 Module 2 Quadratic Functions

2A. 6 Quadratic and square root functions 2A.6 Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to: 2A.6C. determine a quadratic function from its roots or a graph (supporting).

What is the equation of a quadratic function that has zeros -6 and -2? TEKS: 2A.6C

Write a possible equation to match the graph below. Justify your response. TEKS: 2A.6C

Given: x = and x = 1 are the solutions to f(x) = 0. If f(x) = ax 2 + bx + c, and a = 1, what is the value for c ? TEKS: 2A.6C

2A. 6 Quadratic and square root functions 2A.6 Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to: 2A.6A. determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities (readiness);

What is the range of f(x) = (x + 4)2 + 7 ? TEKS: 2A.6A

Determine a minimum viewing window that shows the vertex and intercepts of: y = 4x 2 – 224x + 1692 TEKS: A2.6A

A theater’s nightly profits are modeled by the equation: P(x) = -30x 2 + 420x – 470 Is it possible for the theater to make a nightly profit of $ 1,100? TEKS: A2.6A

The function y = -64(x – 2.50)2 + 400 models a store’s profits in dollars on potato chips where x is the price of a bag of potato chips. What should the store charge for a bag of potato chips to maximize their profits? What is the maximum profit earned? TEKS: A2.6A

2A. 6 Quadratic and square root functions 2A.6 Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to: 2A.6(B) relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions (readiness);

Use the table of values for the quadratic function below to determine between which two x values f(x) will have a zero. TEKS: A2.6B

The values in the table represent points on a parabola. Which of the following must be true? TEKS: A2.6B

Which verbal description best fits the data shown in the graph? TEKS: A2.6B

2A. 7 Quadratic and square root functions 2A.7 Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to: 2A.7A use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a (x - h)2 + k symbolic representations of quadratic functions (readiness); and

How is the h in y = a (x – h)2 + k found from the equation y = ax 2 + bx + c? TEKS: 2A.7A

Write the equation of the function below in standard form: y = x 2 + 6x + 5 y = -x 2 – 6x – 5 y = x 2 – 6x + 5 y = -x 2 + 6x – 5 TEKS: 2A.7A

2A. 7 Quadratic and square root functions 2A.7 Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to: 2A.7(B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a (x - h)2 + k form of a function in applied and purely mathematical situations (supporting).

Sketch a possible graph of the function f(x) = a(x – h)2 + k, if a > 0 and k < 0. Justify your response. TEKS: 2A.7B

Given: f(x) = a (x – h)2 + k is the vertex form of a parabola. If a > 0, h > 0 and k > 0, then which of the four quadrants of a Cartesian plane could f(x) exist in? I and II C. I, IV II and III D. All 4 TEKS: 2A.7B

2A. 8 Quadratic and square root functions 2A.8 Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: 2A.8(A) analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems (readiness)

Mark is building a rectangular fence for his animals. He is using the riverbank as one side and has 120 feet of fencing to use for the other 3 sides. What is the maximum area that he can enclose? TEKS: A2.8A

Max is building a rectangular pen for animals, using the side of a barn as one side. He has 200 feet of fencing to use for the other three sides. What is the maximum area that he can enclose? 10,000 square feet 5,000 square feet 4,800 square feet 3,750 square feet TEKS: A2.8A

Bob kicks a football over an 8-foot fence. The ball barely clears the fence at its maximum height and lands 12 feet from the fence on the other side. Let the y -axis represent the fence and write an equation that approximates the path of the football. What is the height of the ball when it is 9 feet from the fence? (Assume that the ball travels left to right.) TEKS: A2.8A

2A. 8 Quadratic and square root functions 2A.8 Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: 2A.8(B) analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula (supporting);

Solve using the quadratic formula: 2x 2 – 4 = 5x TEKS: A2.8B

Find the discriminant and describe the roots of 25x 2 – 10x + 1 = 0 TEKS: A2.8B

2A. 8 Quadratic and square root functions 2A.8 Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: 2A.8(C) compare and translate between algebraic and graphical solutions of quadratic equations (supporting)

Which of the following functions has a maximum y -value of 3? TEKS: 2A.8C

Greg is looking at the graph of a parabola. Its vertex is (2, -144), it intersects the x -axis at -4 and 8, and it intersects the y -axis at -128. What are the roots of the equation he has graphed? 2 and -144 -4, 8 and -128 -4 and 8 4 and -8 TEKS: 2A.8C

The graph traces the height in feet of an object projected upward at 64 feet per second from an initial height of 6 feet. When is the object about 66 feet high? TEKS: 2A.8C

2A. 8 Quadratic and square root functions 2A.8 Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: 2A.8(D) solve quadratic equations and inequalities using graphs, tables, and algebraic methods (readiness)

Use the given table to determine the solution(s) to g(x) = 0 if g(x) = f(x) + 5 and f(x) = ax 2 + bx + c. TEKS: 2A.8D

Write a possible 2nd step in solving 2x 2 + 2x – 24 = 0 by factoring. TEKS: 2A.8D

A toy rocket is launched into the air at an initial velocity of 64 ft/sec, as shown on the graph below. The function s(t) = -16t 2 + 64t + 80 gives the height of the rocket (in feet) at time t (seconds). When does the rocket hit the ground? TEKS: 2A.8D

A rock is thrown off a bridge into a river. Its height, h meters, t seconds after release is given by h = -4.9t 2 + 6t + 13. How long does it take to hit the water? TEKS: 2A.8D

2A.5 Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to: 2A.5(E) use the method of completing the square (supporting)

If x 2 + 2 = 6x is solved by completing the square, an intermediate step would be: (x + 3)2 = 7 C. (x – 3)2 = 11 (x – 3)2 = 7 D. (x – 6)2 = 34 TEKS: 2A.5E

Brian correctly used a method of completing the square to solve the equation x 2 + 7x – 11 = 0. Brian’s first step was to rewrite the equation as x 2 + 7x = 11. He then added a number to both sides of the equation. What number did he add? TEKS: 2A.5E