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Parabola Regents Practice
By Jeanmarie Mullen
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Last updated almost 5 years ago
29 questions
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Question 1
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Question 2
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Question 3
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Question 4
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Question 5
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Question 6
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Question 7
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Question 8
8.
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Question 9
9.
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Question 10
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Question 11
11.
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Question 12
12.
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Question 13
13.
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Question 14
14.
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Question 15
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Question 16
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Question 17
17.
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Question 18
18.
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Question 19
19.
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Question 20
20.
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Question 21
21.
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Question 22
22.
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Question 23
23.
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Question 24
24.
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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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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
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
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
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
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
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
Which equation represents the axis of symmetry of the graph of the parabola below?
x = -25
y = -3
x = -3
y = -25
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
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
What is the vertex of the graph of the
equation y = 3x
2
+ 6x + 1 ?
(1, 10)
(1, -2)
(-1, -2)
(-1, 10)
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
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
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
The vertex of the parabola
y = x
2
+ 8x + 10 lies in Quadrant
I
II
III
IV
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.
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 .
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.
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
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.
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
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
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
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
Which parabola has an axis of
symmetry of x = 1 ?