Algebra 2 Module 2 Quadratic Functions. 2A.6 Quadratic and square root functions. The student understands that quadratic functions can be represented.

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 ?

52

TEKS: 2A.6C

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 theequation:

P(x) = -30x 2 + 420x – 470

Is it possible for the theater to make a nightly profitof $ 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

TEKS: A2.6B

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: 2A.7A

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:

A. y = x 2 + 6x + 5

B. y = -x 2 – 6x – 5

C. y = x 2 – 6x + 5

D. y = -x 2 + 6x – 5

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 formof a parabola.

If a > 0, h > 0 and k > 0, then which of thefour quadrants of a Cartesian plane couldf(x) exist in?

A. I and II C. I, IVB. II and III D. All 4

TEKS: 2A.7B

TEKS: A2.8A

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?

A. 10,000 square feet

B. 5,000 square feet

C. 4,800 square feet

D. 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.)

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

TEKS: 2A.8C

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?

A. 2 and -144

B. -4, 8 and -128

C. -4 and 8

D. 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?

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 aninitial 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

If x 2 + 2 = 6x is solved by completingthe square, an intermediate step would be:

A. (x + 3)2 = 7 C. (x – 3)2 = 11

B. (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