Deck 3: Quadratic Functions

Question 1

Suppose a quadratic function has vertex (5, 0) and has y-intercept 2. Its formula can be written , where a = _____, and b = _____.

Answer 1

a)2/25
b)5

Question 2

The graph of has vertex ( _____, _____ ) and axis of symmetry x = _____.

Answer 2

a)2
b)3

Question 3

Convert the quadratic function to vertex form. Identify the vertex and the axis of symmetry.

Answer 3

Question 4

Find a formula for the quadratic function whose graph has axis of symmetry , - intercept at , and contains the point .

Question 5

Find a formula for the parabola:

Question 6

The height of a baseball in feet seconds after it has been hit is given by . At what time does the baseball reach maximum height? Give your answer correct to 3 decimal places.

Question 7

The height of a baseball in feet seconds after it has been hit is given by . What is the maximum height of the baseball? Give your answer correct to 3 decimal places.

Question 8

Which of the following parabolas have a vertex of
?

A)

B)

C)

D)

E)

Question 9

Suppose a farmer has 135 feet of fence and he wants to enclose a pasture with a rectangular boundary. There is already fencing along one side of the field that he wants to enclose, so he will only need to fence 3 sides of the new field. What is the maximum area that he can fence?

Question 10

Suppose a farmer has 100 feet of fence and he wants to enclose a pasture with a rectangular boundary. There is already fencing along one side of the field that he wants to enclose, so he will only need to fence 3 sides of the new field. What are the dimension of the field that will give maximum area.

Question 11

What is the equation of the parabola that is concave down, has vertex and contains the origin.

Question 12

Let
a) Graph the function.
b) Give the vertex.
c) Give the axis of symmetry.
d) Give the y-intercept.

Question 13

Find a formula in terms of For .

A)
B)
C)
D)

Question 14

Find a formula for the quadratic function which has only one zero at and contains the point

Question 15

Is the function quadratic? If so, write the function in the form
.

Question 16

How many distinct real roots does the function
have?

Question 17

The vertex form of is , where a = _____ and b = _____.

Question 18

The following figure gives the graph of , a quadratic function with vertex (6, 4). The formula for is , where a = _____, b = _____, and c = _____.

Question 19

A relief package is dropped from an airplane and falls to the ground along a parabolic path, starting at the vertex of the parabola. The package was released when the plane was directly above a marker at a height of 4 kilometers, and the package hits the ground 4.47 kilometers from the marker. If h is the height of the package when it is a horizontal distance d from the marker, the equation for h in terms of d is given by

, where a = _____, b = _____, and c = _____. Round any decimals to 3 places.

Question 20

A projectile's height
Above ground is a quadratic function of time t in seconds since launched. Three values of the function are given in the table below.
What is the practical interpretation of?

A) It is the time it takes the projectile to hit the ground.
B) It is the initial speed of the projectile.
C) It is the height of the projectile above the ground the instant it is fired.
D) It is ground level.

Question 21

A projectile's height above ground is a quadratic function of time t in seconds since launched. Three values of the function are given in the table below. How many seconds does it take for the projectile to hit the ground?

Question 22

A projectile's height above ground in feet is a quadratic function of time t in seconds since launched. Three values of the function are given in the table below. What is the maximum number of feet above the ground that the projectile reaches?

Question 23

The formula for the following parabola is
, where a = _____ , h = _____, and k = _____. Note: Figure is not necessarily drawn to scale.

Question 24

You want to fence in a rectangular area for a dog run along the back of your home. Your home will serve as one side of the run, so you only need to purchase fencing material for the remaining three sides. The fencing material costs $1.50 per foot, and you have a budget of $90.00. How many square feet are in the largest dog run you can afford to build?

Question 25

Find the zeros of by factoring. List the answers in the form "A, B", with A < B.

Question 26

Find the zeros of . List the answers in the form "A, B", with A < B.

Question 27

Which of the following quadratic functions have zeros at x = -5 and x = 2?

A)
B)
C)
D)

Question 28

Solve by the quadratic formula. Round your answers to 2 decimal places. List the answers in the form "A, B", with A < B.

Question 29

If is quadratic, then it can be written as . If is not quadratic, enter "DNE" for each of the blanks.

Question 30

Suppose What is ?

A)
B)
C)
D)

Question 31

Suppose What is ?

A)
B)
C)
D)

Question 32

For , does ?

Question 33

Let be a quadratic function which has y-intercept 0 and has zeros at x = 0 and x = 6. Then .

Question 34

Find a formula for the quadratic function which corresponds to the values in the following table and use it to find g(4).

Question 35

Which of the following functions are quadratic?

A)
B)
C)
D)
E)

Question 36

Find the zeros of by using the quadratic formula. List the answers in the form "A, B", with A < B. Write your answers correct to 3 decimal places

Question 37

The height of an object above the ground is described by the function .
a) What is the initial height of the object at time
t= 0?
b) When does the object have height 3?

Question 38

Find a quadratic equation, , with zeros at and such that
.

Question 39

Which of the following quadratic functions have zeros at And

A)
B)
C)
D)
E)

Question 40

Find a formula for the parabola

Question 41

The height of a baseball in feet seconds after it has been hit is given by
.
a) What is the height of the ball 0.2 seconds after it was hit?
b) When does the ball hit the ground? (If necessary, round your answer to three decimal places)