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Graphing Quadratics Review
Name:
1.
Date:
Which is an equation of the parabola graphed in
the accompanying diagram?
A.
y = x2 + 4
B.
y = x2
C.
y = x2 + 4
4
2.
An equation of the axis of symmetry of the
graph of y = x2 + 6x + 9 is x = 3. What is the
y-coordinate of the turning point?
3.
Which equation can represent the parabola in the
diagram?
y = x2
B.
y = x2
C.
y = x2
3
D. y = x2
4.
Which graph represents the equation y = x2 + 4?
A.
B.
C.
D.
4
D. y = x2
A.
5.
3
Which is an equation of the graph shown in the
diagram?
A.
y = x2
B.
y = x2 + 4
C.
x = y2
4
4
D. x = y2 + 4
page 1
6.
Which graph represents the equation y = x2
3?
7.
The graph of a quadratic equation is shown in the
accompanying diagram. The scale on the axes is
a unit scale. Write an equation of this graph in
standard form.
8.
Which equation represents the parabola shown in
the accompanying graph?
A.
B.
C.
D.
A.
f (x) = (x + 1)2
B.
f (x) = (x
C.
f (x) = (x + 3)2 + 1
D. f (x) = (x
page 2
3
3)2 + 1
3)2
3
Graphing Quadratics Review
9.
10.
Which quadratic function is shown in the
accompanying graph?
A.
y = 2x2
C.
y=
1 2
2x
B.
11.
The equation y = x2 + 3x
set of axes below.
18 is graphed on the
y = 2x2
D. y = 12 x2
Based on this graph, what are the roots of the
equation x2 + 3x 18 = 0?
Consider the graph of the equation y = ax2 + bx + c,
when a 6= 0. If a is multiplied by 3, what is true
of the graph of the resulting parabola?
A.
The vertex is 3 units above the vertex of the
original parabola.
B.
The new parabola is 3 units to the right of
the original parabola.
C.
The new parabola is wider than the original
parabola.
A.
C.
12.
3 and 6
3 and
6
The equation y = x2
set of axes below.
B.
0 and
18
D. 3 and
18
2x + 8 is graphed on the
D. The new parabola is narrower than the
original parabola.
Based on this graph, what are the roots of the
equation x2 2x + 8 = 0?
page 3
A.
8 and 0
C.
9 and
B.
1
2 and
4
D. 4 and
2
Graphing Quadratics Review
13.
The diagram below shows the graph of y = x2
Which diagram shows the graph of y = x2
c.
c?
A.
B.
C.
D.
page 4
Graphing Quadratics Review
14.
The graph of a parabola is represented by the
equation y = ax2 where a is a positive integer. If a
is multiplied by 2, the new parabola will become
A.
narrower and open downward
B.
narrower and open upward
C.
wider and open downward
15.
The roots of a quadratic equation can be found
using the graph below.
D. wider and open upward
What are the roots of this equation?
16.
17.
18.
A.
4, only
B.
4 and
C.
1 and 4
D.
4,
page 5
1, and 4
What is the turning point of the parabola whose
equation is y = 2x2 + 4x 3?
A.
(1; 3)
B.
C.
(2; 13)
D. ( 1; 5)
( 2; 3)
What are the coordinates of the turning point of
the parabola whose equation is y = x2 2x 4?
A.
( 2; 4)
B.
C.
( 1; 1)
D. (2; 4)
(1; 5)
The coordinates of the turning point of the graph
of y = x2 + 4x + q are ( 2; 7). The value of q is
A.
19.
1
1
B.
2
C.
3
D.
17
The coordinates of the turning point of the graph
of the equation y = x2 2x 8 are (1; k). What is
the value of k ?
Graphing Quadratics Review
20.
21.
22.
23.
24.
25.
What are the coordinates of the turning point of
the parabola whose equation is y = x2 6x + 5?
A.
( 3; 4)
B.
C.
(3; 14)
D. (3; 4)
26.
Which is an equation of the line of symmetry for
the parabola in the accompanying diagram?
( 3; 32)
What is the turning point of the parabola whose
equation is y = x2 4x + 3?
A.
( 2; 1)
B.
( 2; 7)
C.
(2; 9)
D. (2; 1)
What is the turning point, or vertex, of the
parabola whose equation is y = 3x2 + 6x 1?
A.
(1; 8)
B.
( 1; 4)
C.
( 3; 8)
D. (3; 44)
A.
27.
Which is an equation of the axis of symmetry of
the parabola whose equation is y = 3x2 12x 13?
A.
x= 4
B.
x=2
C.
x=3
D. x = 4
x=2
B.
x=4
C.
x=3
D. y = 3
For which quadratic equation is the axis of
symmetry x = 3?
A.
y = x2 + 3x + 5
B.
y = x2 + 6x + 2
C.
y = x2 + 6x + 3
D. y = x2 + x + 3
Which is an equation of the axis of symmetry of
the parabola whose equation is y = 2x2 3x + 4?
A.
x=
3
4
B.
x=
3
4
C.
y=
3
4
D. y =
3
4
Which is the axis of symmetry of the graph of the
equation y = x2 2x 1?
A.
x= 1
B.
y= 1
C.
x=1
D. y = 1
page 6
Graphing Quadratics Review
28.
What are the vertex and the axis of symmetry of
the parabola shown in the diagram below?
A.
The vertex is ( 2; 3), and the axis of
symmetry is x = 2.
B.
The vertex is ( 2; 3), and the axis of
symmetry is y = 2.
C.
The vertex is ( 3; 2), and the axis of
symmetry is y = 2.
30.
What is the equation of the axis of symmetry of
the parabola shown in the diagram below?
A.
x = 0:5
B.
x=2
C.
x = 4:5
D. x = 13
D. The vertex is ( 3; 2), and the axis of
symmetry is x = 2.
29.
What are the vertex and axis of symmetry of the
parabola y = x2 16x + 63?
A.
vertex: (8; 1); axis of symmetry: x = 8
B.
vertex: (8; 1); axis of symmetry: x = 8
C.
vertex: ( 8; 1); axis of symmetry: x = 8
D. vertex: ( 8; 1); axis of symmetry: x = 8
page 7
Graphing Quadratics Review
31.
Which parabola has an axis of symmetry of x = 1?
32.
A.
What is the y-intercept of the graph of the
equation y = x2 2x + 3?
A.
33.
34.
B.
35.
C.
36.
D.
38.
B.
2
C.
3
D.
2
What is the y-intercept of the graph of the
parabola whose equation is y = x2 2x 8?
A.
(4; 0)
B.
C.
( 8; 0)
D. (0; 8)
(0; 4)
What are the coordinates of the minimum point of
a parabola whose equation is y = x2 + 2?
A.
(0; 3)
B.
C.
(3; 0)
D. (3; 12)
( 1; 2)
Which is an equation of the parabola that intersects
the x-axis at the points (2; 0) and (5; 0)?
A.
y = x2 + 7x + 10
B.
C.
y = x2
D. y = x2
7x + 10
y = x2 + 10x + 7
10x + 7
Which point is on the graph of the parabola whose
equation is y = 2x2 3x + 4?
A.
37.
1
(0; 3)
B.
(3; 0)
C.
(4; 0)
D. (0; 4)
Which is an equation of a parabola which does
not pass through the origin?
A.
y = 12 x2
C.
y = x2
B.
2x + 2
y = x2
2x
D. y = 2x2
Which is true of the graph of the parabola whose
equation is y = x2 2x 8 ?
A.
The x-intercepts are at x = 2 and x = 4.
B.
The only x-intercept is at x = 4.
C.
The x-intercepts are at x = 4 and x = 2.
D. There are no x-intercepts.
page 8
Graphing Quadratics Review
39.
40.
The graph of which equation contains a maximum
point?
A.
y=2
B.
C.
y = x2
D. y = x2
41.
y= 2
The accompanying diagram shows a parabola.
How is the graph of y = x2 + 4x + 3 a ected
when the coe cient of x2 is changed to a smaller
positive number?
A.
The graph becomes wider, and the y-intercept
changes.
B.
The graph becomes wider, and the y-intercept
stays the same.
C.
The graph becomes narrower, and the
y-intercept changes.
D. The graph becomes narrower, and the
y-intercept stays the same.
42.
Which statement is not true?
Which is the equation of a parabola that has the
same vertex as the parabola represented by y = x2 ,
but is wider?
A.
The equation of the axis of symmetry is
x = 2.
A.
y = x2 + 2
B.
B.
The parabola has a minimum point.
C.
y = 2x2
D. y = 12 x2
C.
The turning point of the parabola is ( 2; 1).
y = x2
2
D. The parabola has two x-intercepts.
page 9
Graphing Quadratics Review
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Graphing Quadratics Review
21.
Answer:
1.
Answer:
C
2.
Answer:
0
3.
Answer:
D
4.
Answer:
B
5.
Answer:
B
6.
Answer:
C
22.
Answer:
24.
Answer:
26.
Answer:
27.
Answer:
y=
8.
Answer:
C
9.
Answer:
B
10.
Answer:
D
11.
Answer:
C
12.
Answer:
B
13.
Answer:
A
14.
Answer:
B
15.
Answer:
C
16.
Answer:
D
17.
Answer:
B
18.
Answer:
C
20.
Answer:
23.
Answer:
25.
Answer:
7.
Answer:
19.
Answer:
05/01/2015
x2
+ 3x
18
28.
Answer:
29.
Answer:
30.
Answer:
31.
Answer:
32.
Answer:
33.
Answer:
34.
Answer:
35.
Answer:
36.
Answer:
37.
Answer:
38.
Answer:
39.
Answer:
40.
Answer:
9
D
41.
Answer:
42.
Answer:
B
B
B
B
A
C
B
A
A
B
A
C
D
A
C
D
C
C
D
D
B
D