1
Determine the axis of symmetry of this quadratic function.
-6
-4
-2
2
4
6
8
10
x
-8
-6
-4
-2
2
4
6
8
y
2
Write an equation for each quadratic function in vertex form.
a
-8
-7
-6
-5
-4
-3
-2
-1
1
2
x
-2
2
4
6
8
10
12
14
16
y
b
-2
-1
1
2
3
4
5
6
7
8
x
-14
-12
-10
-8
-6
-4
-2
2
y
c
| x | h(x) |
| 0 | -6 |
| 1 | -1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 2 |
| 5 | -1 |
| 6 | -6 |
d
| x | j(x) |
| -6 | 11 |
| -5 | 6 |
| -4 | 3 |
| -3 | 2 |
| -2 | 3 |
| -1 | 6 |
| 0 | 11 |
3
For the following quadratic equations:
i
Rewrite the equation in vertex form by completing the square.
ii
Identify the coordinates of the vertex.
a
y = x^{2} - 4 x + 3
b
y = - x^{2} + 6 x - 2
c
y = - x^{2} - 5 x - 4
d
y = - 2 x^{2} + 8 x - 7
4
Write the equation of the transformed graph in vertex form.
a
y = x^{2} is horizontally translated 10 units to the right and vertically translated 2 units up
b
y = x^{2} is horizontally translated 9 units to the left and is vertically stretched by a factor of 9 units
c
y = x^{2} is reflected across the x-axis and vertically translated 8 units down
5
For each of the following, state whether the transformation from the parent function f(x)=x^2 to the function g(x) is a translation up, down, left, or right:
a
g(x)=(x-8)^{2}
b
g(x)=x^{2}-5
c
g(x)=(x+9)^{2}
d
g(x)=x^{2}+0.75
6
Consider the following graph of a function.
Select the equation that represents the function:
A
y = -\left(x + 5\right)^{2} + 25
B
y = \left(x - 5\right)^{2} + 25
C
y = \left(x + 5\right)^{2} - 25
D
y = -\left(x + 5\right)^{2} - 25
-12
-10
-8
-6
-4
-2
2
x
-25
-20
-15
-10
-5
5
y
7
Consider the table of values of a function.
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | -6 | 0 | 2 | 0 | -6 |
Sketch a graph of the function labeling any points of interest.
8
Consider the function y = \dfrac{1}{4} \left(x + 4\right)^{2} + 5.
Sketch a graph of the function labeling any points of interest.
9
For each of the following:
i
Rewrite the equation in vertex form.
ii
Sketch the graph of the parabola.
a
y = x^{2} - 4 x + 2
b
y = x^{2} + 10 x
c
y = x^{2} + 4 x - 4
d
y = x^{2} + 5 x + 3
10
Explain how the maximum or minimum value of a quadratic function can be found by completing the square.
11
For each of the following quadratic functions:
i
State whether the transformation from f(x) to
g(x) is a horizontal translation, vertical translation, vertical stretch, or vertical compression by
k units.
ii
State the value of k.
a
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
b
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
c
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
12
For each quadratic function:
i
Determine the coordinates of the vertex.
ii
Determine the x-intercept.
iii
Determine the y-intercept.
iv
Draw a graph of the quadratic function.
a
m \left( x \right) = \left(x - 3\right)^{2}
b
n(x) = \left(x + 4\right)^{2} - 1
c
p(x) = - \left(x - 1\right)^{2} - 7
d
r(x) = 3 \left(x + 5\right)^{2}
13
Rodney observed that the water stream of a fountain is in the shape of a parabola. This water stream lands on an underwater spotlight. He models the path of the water stream with the maximum height of 8 feet, represented by the vertex \left(4, 8 \right) and the underwater spotlight, represented by the point \left( 8, 0 \right).
a
Select the graph that represents the problem:
A
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
B
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
C
2
4
6
8
10
12
14
16
18
x
1
2
3
4
5
6
7
8
9
y
D
-16
-12
-8
-4
4
8
12
16
x
-8
-6
-4
-2
2
4
6
8
y
b
Determine appropriate labels and units for the axes.
c
Determine the domain and range of the function.
14
For each quadratic equation:
i
Determine the coordinates of the vertex.
ii
Determine the equation of the axis of symmetry.
iii
Determine if it has a maximum or minimum.
iv
Determine the domain and range.
v
Draw a graph of the quadratic function.
a
y = -\dfrac{1}{2} \left(x - 4\right)^{2}+1
b
y = 5 \left(x - \dfrac{1}{4}\right)^{2} - 20
15
Ashtyn throws a rock into Crescent Lake. The height of the rock above ground is a quadratic function of time. The rock is thrown from
4.4 \text{ ft} above ground. After
1.5 seconds, the rock reaches its maximum height of
24 \text{ ft}. Write the quadratic equation in vertex form.
16
A roller coaster has a part that is modeled by a quadratic function. Hau loves roller coasters and wants to be able to build a small model with his 3D Printer. Assume that the roller coaster passes through points \left(0,0\right) and \left(57,0\right) and reaches a maximum height of 90 \text{ ft}. Help Hau build a model of the roller coaster by writing an equation for the parabola in vertex form.
17
Karima and Riley are playing soccer. Karima just kicked a soccer ball and Riley is playing goalie 2 \text{ ft} in front of the goal post. The following diagram shows the situation on a coordinate plane. The soccer ball is kicked at (1, 0.6) and the goal post is 13 \text{ ft} away from Karima's back foot. The maximum height of the soccer ball is 5.5 \text{ ft} and this occurs when it is 8 \text{ ft} away from Karima.
a
Write a quadratic function that models the height of the soccer ball in feet in terms of the horizontal distance from Karima's starting position.
b
Riley jumps to try to block the soccer ball and will block soccer balls that are between 4 \text { ft} and
8 \text{ ft} high. State whether Riley will be able to block Karima's kick. Explain your answer.
18
Determine how many quadratic equations could share a common vertex.
19
Consider the following diagram:
a
Describe a situation that could be modeled by the following three quadratic functions. For each part, make sure to identify the vertex and another possible point on the function.
b
Write equations for the quadratic functions from your above description.
20
Consider the family of quadratic equations of the form y=⬚(x-⬚)^2-⬚ where the boxes contain the integers 2, 3, and 5.
a
Write a quadratic equation with the lowest possible minimum value.
b
Describe the similarities and differences between members of the family.
21
Compare and contrast the following functions, given that a is a positive real number:
f(x)=-3a(x-h)^2+k \text{ and }g(x)=a(x-h)^2-k
