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Parabola Regents Practice

Last updated over 4 years ago
29 questions
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?

1

The equation y = -x2 - 2x + 8
is graphed on the set of axes below.

Based on this graph, what are the
roots of the equation -x2 - 2x + 8 = 0 ?

1

The height, y , of a ball tossed into the air can be
represented by the equation y = -x2 + 10x + 3 ,
where x is the elapsed time. What is the equation
of the axis of symmetry of this parabola?

1

What are the vertex and the axis of symmetry of the parabola shown in the graph below?

1

What are the coordinates of the vertex and the equation of the axis of symmetry of the parabola shown in the graph below?

1

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?

1

Which equation represents the axis of symmetry of the graph of the parabola below?

1

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?

1

What is an equation of the axis of symmetry
of the parabola represented
by y = -x2 + 6x - 4 ?

1

What is the vertex of the graph of the
equation y = 3x2 + 6x + 1 ?

1

The graph of f(x) is shown below.

Based on this graph, what are the
roots of the equation f(x) = 0 ?

1

Which equation represents the axis of
symmetry of the graph of the
equation y = x2 + 4x - 5 ?

1

A model rocket is launched into the air from ground level.
The height, in feet, is modeled by p(x) = -16x2 + 32x ,
where x is the number of elapsed seconds. What is the
total number of seconds the model rocket will be in the air?

1

The vertex of the parabola
y = x2 + 8x + 10 lies in Quadrant

1

How is the graph of y = x2 + 4x + 3
affected when the coefficient of x2
is changed to a smaller positive number?

1

What are the vertex and the axis of symmetry of the parabola shown in the diagram below?

1

Consider the graph of the equation
y = ax2 + 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?

1

What are the vertex and axis of symmetry of the parabola shown in the diagram below?

1

Melissa graphed the equation y = x2
and Dave graphed the equation y = -3x2
on the same coordinate grid. What is the
relationship between the graphs that Melissa and Dave drew?

1

What are the vertex and axis of symmetry
of the parabola y = x2 - 16x + 63 ?

1

The equation y = x2 + 3x - 18
is graphed on the set of axes below.

Based on this graph, what are the
roots of the equation x2 + 3x - 18 = 0 ?

1

The roots of a quadratic equation can be found using the graph below.

What are the roots of this equation?

1

The equation y = ax2 + bx + c
is graphed on the set of axes below.

Based on the graph, what are the roots
of the equation ax2 + bx + c = 0 ?

1

Which parabola has an axis of
symmetry of x = 1 ?

1

State the equation of the axis of symmetry of the parabola graphed below.

1

State the coordinates of the vertex of the parabola graphed below.

1

Find algebraically the equation of the axis
of symmetry of the parabola whose
equation is y = -2x2 - 8x + 3 .

1

Find algebraically the coordinates of the
vertex of the parabola whose equation is
y = -2x2 - 8x + 3 .

1

Graph the equation y = x2 - 2x - 3
on the accompanying set of axes.

Using the graph, determine the roots
of the equation x2 - 2x - 3 = 0 .

(Write your answer such as
8and9
-7and-4 )