Chapter 9.1-9.4 Test Review due on the day of the test. NO WORK, NO CREDIT
 Review will not be graded unless answers are written on separate paper.
 Eligibility to retest: complete accurate review, all homework and missing assignments must be
turned in prior to retesting. Tutoring is required. Retesting window is 1 week following return
of original test.
1. Tell whether the function is quadratic. Explain.
x
0
2
4
y
21
1
9
37
2. Tell whether the graph of the quadratic function
3. Tell whether the graph of the quadratic function
opens upward or downward. Explain.
opens upward or downward. Explain.
4. A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with uniform width x. Write a quadratic
function in standard form to show the combined area of the picture and frame.
5. Find (1)the axis of symmetry (2)the vertex and (3) the zeros of the parabola
.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
6. Find (1)the axis of symmetry (2)the vertex and (3) the zeros of the parabola
.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
7. Find the axis of symmetry and the vertex of the parabola
8. Find the axis of symmetry and the vertex of the parabola
.
.
9. Graph y = –x2 – 4x – 3.
10. Graph y = 2x2 + 2x + 1.
11. The height of a soccer ball that is kicked from the ground can be approximated by the function
, where y is the height of the soccer ball in feet x seconds after it is kicked. Graph this function. Find the time it
takes the soccer ball to reach its maximum height, the soccer ball’s maximum height, and the time it takes the
soccer ball to return to the ground.
12. The height of a curved support beam can be modeled by
. Find the height and width of the
beam.
height
width
x.
13. Order the functions from narrowest graph to widest graph.
,
, and
14. Order the group of quadratic functions from widest to narrowest graph.
,
,
15. Compare the graph of
 2 x2 – 2 with the parent graph of
16. Compare the graph of
3x2 + 4 with the parent graph of
17. What is the equation of
1
.
.
after it has been translated down 6 units? How will the new (x, y) change?
____ 18. Which of the quadratic functions has the narrowest graph?
a.
b.
c.
d.
____ 19. Which of the quadratic functions has the widest graph?
a.
b.
c.
d.
____ 20. A parabola ________ has an axis of symmetry.
a. always
b. sometimes
c. never
Spiral Exam: Study your reviews from chapter tests 1 through 8(also on my web site), review the textbook
reviews, and come in for tutoring!
 Understand how to determine if data is a function.
 determine what equation models a set of data
 ( )
given the set {0, 3, 5, 7} for the independent variable, what is the corresponding set of
values for the dependent variable?
 Review function notation, dependent and independent variables
 Solving and graphing inequalities, when do > and< flip? When is the line dashed vs. solid?
 Parallel and perpendicular lines, what are the rules/relationships regarding their slopes?
y
Chapter 9.1-9.4 Text Review
Answer Section
10
8
6
1. Yes, the function is quadratic. The second
differences are constant.
OBJ: 9-1.1 Identifying Quadratic Functions
2. Because
, the parabola opens upward.
OBJ: 9-1.3 Identifying the Direction of a
Parabola
3. Because
, the parabola opens
downward.
OBJ: 9-1.3 Identifying the Direction of a
Parabola
4.
5. ANS: x=--3, (–3, 2), {-4, -2}
OBJ: 9-2.4 Finding the Vertex of a Parabola
6. x=4, (4, –2), {3, 5}
OBJ: 9-2.4 Finding the Vertex of a Parabola
7. (5, –9)
OBJ: 9-2.4 Finding the Vertex of a Parabola
8. (–6.5, 4.5)
OBJ: 9-2.4 Finding the Vertex of a Parabola
9. ANS:
4
2
–10 –8
–6
–4
–2
–2
2
4
6
x
8
–4
–6
–8
–10
OBJ: 9-3.1 Graphing a Quadratic Function
11.
50
y
40
30
20
y
10
10
8
6
1
2
3
4
5
6
7
8
9
x
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
x
–4
–6
–8
It takes the ball 1.5 seconds to reach its
maximum height. The ball’s maximum
height is 36 feet. It takes the ball 3 seconds to
return to the ground.
OBJ: 9-3.2 Problem-Solving Application
12. height = 12 units; width = 120 units
13.
–10
OBJ: 9-3.1 Graphing a Quadratic Function
,
,
OBJ: 9-4.1 Comparing Widths of Parabolas
14.
,
,
OBJ: 10-1.1 Graphing y = ax^2
15. The graph of
the graph of
 2 x2 – 2 is wider than
1
. The graph of
 x – 2 opens downward, and the graph of
1
2
2
opens upward. The axis of
symmetry is the same. The vertex of
is (0, 0). The vertex of
10.ANS:
2
1
x2 – 2 is translated down 2 units to (0, –2).
OBJ: 9-4.2 Comparing Graphs of Quadratic
Functions
16. The graph of
 4 x2 + 4 is wider than
3
the graph of
. The graph of
 x + 4 opens downward, and the graph of
3
4
2
opens upward. The axis of
symmetry is the same. The vertex of
is (0, 0). The vertex of
4
3
x2 + 4 is translated up 4 units to (0, 4).
OBJ: 9-4.2 Comparing Graphs of Quadratic
Functions
17.
,
18. ANS: C
OBJ: 10-1.1
Graphing y = ax^2
19. ANS: C
OBJ: 10-1.1
Graphing y = ax^2
20. ANS: A
OBJ: 10-1.2
Graphing y = ax^2 + c