Name______________________________________________ Date ______________________ Period __________
Unit 9 – Properties of Quadratic Functions
Study Guide
1. The function 𝑔(𝑥) = 𝑥 2 + 4𝑥 – 5 is graphed below
Answer parts A-E:
A) What are the zeros of function 𝑔?
B) What is the minimum value of 𝑔?
C) What is the vertex of 𝑔?
D) What is the axis of symmetry for 𝑔?
E) Give the domain and range for function 𝑔.
3. The graph of a quadratic function is shown below
2. Two points on the graph of a
quadratic function are shown on the
grid below
Which statement about this graph is not true?
What is the equation of the axis of
symmetry for the graph of the
function?
A
The graph has a y-intercept at (0, 0)
B
The graph has an axis of symmetry at x = −3
C
The graph has an x-intercept at (−6, 0)
D
The graph has a maximum point at (−3, −3)
4. Answer the 3 questions below using the quadratic function 𝑓(𝑥) = 2𝑥 2 − 5𝑥 − 3. (Part A has multiple choice answers)
A) What are the x-intercepts of the graph of 𝑓? A
1
2
𝑎𝑛𝑑 − 3
1
B 0 𝑎𝑛𝑑 3
C − 2 𝑎𝑛𝑑 3
B) What is the axis of symmetry for 𝑓?
C) Tell if 𝑓 has a maximum or minimum and give the value.
5. The table shows some ordered pairs that belong to quadratic function 𝑝. (A.6A)
x
0
1
2
3
4
5
7
y
34
20
10
4
2
4
20
What is the range of 𝑝?
D
1
2
𝑎𝑛𝑑 3
6. f(x) = 1,600 − x2 models the path of a skydiver
before he opens his parachute. What is a
reasonable domain and range for f(x)?
A
0 ≤ 𝑥 ≤ 40
C
0 ≤ 𝑦 ≤ 1,600
B
0 ≤ 𝑥 ≤ 1,600
x = all real
𝑦 < 1,600
D
0 ≤ 𝑦 ≤ 40
7. f(x) = 8,100 − x2 models the number of bees in
a hive over a period of months. The number of
bees is declining. What is a reasonable domain
and range for f(x)?
−90 < 𝑥 < 90
A
x = all real
C
𝑦 ≤ 8,100
𝑦 ≤ 8,100
−40 < 𝑥 < 40
B
𝑦 < 1,600
0 ≤ 𝑥 ≤ 90
D
𝑥 > 0
0 ≤ 𝑦 ≤ 8,100
8. The graph below shows the path of a sub.
9.
0 < y < 80
D
12.How does the graph of 𝑓(𝑥) = 𝑥2 differ from the
graph of 𝑔(𝑥) =
B
0 < y < –300
10. Give the domain and range for the quadratic function
𝑦 = −2𝑥 2 − 4𝑥 + 7
The graph of 𝑔 is wider than the graph of 𝑓.
B
The graph of 𝑔 is narrower than the graph of 𝑓.
C
The vertex of the graph of 𝑔 is 3 units
higher.
D
The vertex of the graph of 𝑔 is 3 units
Lower.
14. Write a quadratic function that transforms the
graph of the parent function, 𝑓(𝑥) = 𝑥 2 , right 7
units and down 4 units.
0 ≤ x ≤ 10
D
0≤x ≤8
11.Give the domain and range for the quadratic function
𝑦 = 𝑥 2 − 4𝑥 + 6
13. How does the graph of y =
1 2
𝑥 ?
3
A
The graph below shows a soccer ball’s path.
What is the domain of this function?
0 < x < 10
0 < x< 8
A
C
What is the range of this function?
0 ≤ y ≤ 80
0 ≤ y ≤ –300
A
C
B
0 < 𝑦 < 8,100
2𝑥 2 differ from the
graph of y = 5𝑥2 ?
A
The vertex of the graph of y = 2𝑥 2 is 3 units
higher.
B
The vertex of the graph of y = 2𝑥 2 is 3 units
lower.
C
The graph of y = 2𝑥 2 is wider.
D
The graph of y = 2𝑥 2 is narrower.
15. Write a quadratic function that makes the
parent function, 𝑓(𝑥) = 𝑥 2 , wider by a factor of
and shift left 5 units.
1
3
16. Quadratic functions 𝑓 and 𝑔 are graphed on the same coordinate grid. The
vertex of the graph of 𝑓 is 3 units to the right of the vertex of graph 𝑔. Which
pair of functions could have been used to create the graphs of 𝑓 and 𝑔?
17. Quadratic functions 𝑓 and 𝑔 are graphed on the same coordinate grid. The
vertex of the graph of 𝑓 is 3 units below the vertex of graph 𝑔. Which pair of
functions could have been used to create the graphs of 𝑓 and 𝑔?
Use these answer choices to answer
#16 and 17
A
𝑓(𝑥) = 𝑥 2 + 3 and 𝑔(𝑥) = 𝑥 2
B
𝑓(𝑥) = (𝑥 + 3)2 and 𝑔(𝑥) = 𝑥 2
C
𝑓(𝑥) = (𝑥 − 3)2 and 𝑔(𝑥) = 𝑥 2
D
𝑓(𝑥) = 𝑥 2 − 3 and 𝑔(𝑥) = 𝑥 2
Use the word bank on the right to fill in the blanks.
Functions ℎ is in the form of ℎ(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘.
18. If the value of 𝑎 is less than 0 the parabola will open ___________
19. If the value of 𝑎 is greater than 0 the parabola will open __________
20. If the value of 𝑘 is less than 0 the vertex of the parabola will be ____________of the x-axis
21. If the value of 𝑘 is greater than 0 the vertex of the parabola will be ____________ of the x-axis
Word Bank:
Up
Down
Left
Right
Above
Below
22. If the value of ℎ is less than 0 the vertex of the parabola will be on the ____________of the y-axis
23. If the value of ℎ is greater than 0 the vertex of the parabola will be on the ____________ of the y-axis
24. Write the equation of the quadratic function below in vertex
form 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, given a vertex of (-4, -3) and
the point (-5 , -4).
25. Write the equation of the quadratic function below in vertex
form 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, given a vertex of (2, 0) and the
point (1, 2).
26. Write the equation of the quadratic function below in vertex
form 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, given a vertex of (0, -5) and
the point (1 , -8).
27. Write the equation of the quadratic function below in vertex
form 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, given a vertex of (-3, 2) and
the point(-2, 4).
28. Write 𝑓(𝑥) = −2(𝑥 − 4)2 + 5 in the standard form 𝑓(𝑥) =
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
29. Write 𝑓(𝑥) = −(𝑥 + 2)2 − 3 in the standard form 𝑓(𝑥) =
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
Factoring Practice – skip numbers 2, 5, 13, 18, 19, 20