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Parabola Regents Practice
By Jeanmarie Mullen
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Last updated over 4 years ago
29 questions
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Question 1
1.
A swim team member performs a dive from a 14-foot-high springboard.
The parabola below shows the path of her dive.
Which equation represents the axis of symmetry?
x = 23
x = 3
y = 3
y = 23
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Question 2
2.
The equation y = -x
2
- 2x + 8
is graphed on the set of axes below.
Based on this graph, what are the
roots of the equation -x
2
- 2x + 8 = 0 ?
9 and -1
4 and -2
8 and 0
2 and -4
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Question 3
3.
The height, y , of a ball tossed into the air can be
represented by the equation y = -x
2
+ 10x + 3 ,
where x is the elapsed time. What is the equation
of the axis of symmetry of this parabola?
x = 5
y = 5
y = -5
x = -5
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Question 4
4.
What are the vertex and the axis of symmetry of the parabola shown in the graph below?
vertex: (6, 1) ; axis of symmetry: x = 1
vertex: (1, 6) ; axis of symmetry: y = 1
vertex: (1, 6) ; axis of symmetry: x = 1
vertex: (6, 1) ; axis of symmetry: y = 1
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Question 5
5.
What are the coordinates of the vertex and the equation of the axis of symmetry of the parabola shown in the graph below?
(-2, 6) and y = -2
(0, 2) and y = 2
(0, 2) and x = 2
(-2, 6) and x = -2
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Question 6
6.
The graph below represents the parabolic path of a ball kicked by a young child. What are the vertex and the axis of symmetry for the parabola?
vertex: (8, 3) ; axis of symmetry: y = 3
vertex: (8, 3) ; axis of symmetry: x = 3
vertex: (3, 8) ; axis of symmetry: x = 3
vertex: (3, 8) ; axis of symmetry: y = 3
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Question 7
7.
Which equation represents the axis of symmetry of the graph of the parabola below?
x = -25
y = -3
x = -3
y = -25
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Question 8
8.
A student correctly graphed the parabola shown below to solve a given quadratic equation.
What are the roots of the quadratic equation associated with this graph?
-3 and 2
-2 and 3
-6 and 3
-6 and 0
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Question 9
9.
What is an equation of the axis of symmetry
of the parabola represented
by y = -x
2
+ 6x - 4 ?
y = 6
y = 3
x = 3
x = 6
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Question 10
10.
What is the vertex of the graph of the
equation y = 3x
2
+ 6x + 1 ?
(1, 10)
(1, -2)
(-1, -2)
(-1, 10)
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Question 11
11.
The graph of f(x) is shown below.
Based on this graph, what are the
roots of the equation f(x) = 0 ?
1 and -5
-1 and 5
-1 and -5 and 5
2 and -9
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Question 12
12.
Which equation represents the axis of
symmetry of the graph of the
equation y = x
2
+ 4x - 5 ?
x = -2
x = 4
y = 4
y = -2
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Question 13
13.
A model rocket is launched into the air from ground level.
The height, in feet, is modeled by p(x) = -16x
2
+ 32x ,
where x is the number of elapsed seconds. What is the
total number of seconds the model rocket will be in the air?
0
16
2
1
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Question 14
14.
The vertex of the parabola
y = x
2
+ 8x + 10 lies in Quadrant
I
II
III
IV
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Question 15
15.
How is the graph of y = x
2
+ 4x + 3
affected when the coefficient of x
2
is changed to a smaller positive number?
The graph becomes narrower, and the y-intercept stays the same.
The graph becomes wider, and the y-intercept changes.
The graph becomes wider, and the y-intercept stays the same.
The graph becomes narrower, and the y-intercept changes.
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Question 16
16.
What are the vertex and the axis of symmetry of the parabola shown in the diagram below?
The vertex is (-3, -4) , and the axis of symmetry is x = -2 .
The vertex is (-2, -4) , and the axis of symmetry is x = -2 .
The vertex is (-3, -4) , and the axis of symmetry is y = -2 .
The vertex is (-2, -4) , and the axis of symmetry is y = -2 .
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Question 17
17.
Consider the graph of the equation
y = ax
2
+ bx + c , when a is NOT equalt to 0.
If a is multiplied by 3, what is true of
the graph of the resulting parabola?
The new parabola is 3 units to the right of the original parabola.
The vertex is 3 units above the vertex of the original parabola.
The new parabola is narrower than the original parabola.
The new parabola is wider than the original parabola.
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Question 18
18.
What are the vertex and axis of symmetry of the parabola shown in the diagram below?
vertex: (-4, 1) ; axis of symmetry: x = -4
vertex: (1, -4) ; axis of symmetry: x = -4
vertex: (1, -4) ; axis of symmetry: x = 1
vertex: (-4, 1) ; axis of symmetry: x = 1
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Question 19
19.
Melissa graphed the equation y = x
2
and Dave graphed the equation y = -3x
2
on the same coordinate grid. What is the
relationship between the graphs that Melissa and Dave drew?
Dave's graph is wider and is three units below Melissa's graph.
Dave's graph is wider and opens in the opposite direction from Melissa's graph.
Dave's graph is narrower and is three units to the left of Melissa's graph.
Dave's graph is narrower and opens in the opposite direction from Melissa's graph.
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Question 20
20.
What are the vertex and axis of symmetry
of the parabola y = x
2
- 16x + 63 ?
vertex: (-8, 1) ; axis of symmetry: x = -8
vertex: (8, -1) ; axis of symmetry: x = 8
vertex: (-8, -1) ; axis of symmetry: x = -8
vertex: (8, 1) ; axis of symmetry: x = 8
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Question 21
21.
The equation y = x
2
+ 3x - 18
is graphed on the set of axes below.
Based on this graph, what are the
roots of the equation x
2
+ 3x - 18 = 0 ?
3 and -18
3 and -6
-3 and 6
0 and -18
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Question 22
22.
The roots of a quadratic equation can be found using the graph below.
What are the roots of this equation?
-4 and -1
-1 and 4
-4, only
-4, -1, and 4
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Question 23
23.
The equation y = ax
2
+ bx + c
is graphed on the set of axes below.
Based on the graph, what are the roots
of the equation ax
2
+ bx + c = 0 ?
0 and 5
3 and -4
1 and 5
1 and 0
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Question 24
24.
Which parabola has an axis of
symmetry of x = 1 ?
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Question 25
25.
State the equation of the axis of symmetry of the parabola graphed below.
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Question 26
26.
State the coordinates of the vertex of the parabola graphed below.
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Question 27
27.
Find algebraically the equation of the axis
of symmetry of the parabola whose
equation is y = -2x
2
- 8x + 3 .
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Question 28
28.
Find algebraically the coordinates of the
vertex of the parabola whose equation is
y = -2x
2
- 8x + 3 .
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Question 29
29.
Graph the equation y = x
2
- 2x - 3
on the accompanying set of axes.
Using the graph, determine the roots
of the equation x
2
- 2x - 3 = 0 .
(Write your answer such as
8and9
-7and-4 )
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