WorksheetsA2-CHAPTER 2 TEST 2023-2024
Total questions: 167
Worksheet time: 6hrs 59mins
Where the parabola (U shape) crosses the x-axis.
Domain
Range
Y-intercept
X-intercept
An equation that can be written in the form y = ax2 + bx + c
Quadratic equation
Polynomical equation
Linear equation
Maxical equation
A vertical line that cuts the parabola into 2 symmetrical halves. This always goes through the vertex and ALWAYS begins with "x=" This is sometimes called the "line of symmetry".
Parabola
Quadratic
Axis of Symmetry
Domain
Where the parabola crosses the y-axis.
X-intercept
Domain
Y-intercept
Axis of Symmetry
The vertex is defined as:
The maximum.
The minimum.
The highest or lowest point of the parabola.
The vertical height of the parabola
If the vertex is the highest point of the parabola, it is called a _______________.
valley
peak
minimum
maximum
If the vertex is the lowest point of the parabola, it is called a ________________.
valley
peak
minimum
maximum
What is the green dashed line called?
roots or x-intercepts
parabola
axis of symmetry
y intercept
What is the significance of the ordered pair (0, -2) to the graph?
It is the vertex
It is an x-intercept
It is the y-intercept
It is the axis of symmetry
Is this parabola a maximum or minimum?
maximum
minimum
cannot be determined
The highest or lowest point on the parabola
Parabola
Domain
Vertex
Range
What are the x-intercept(s) of this graph?
-1 and -3
-1 and 3
1 and 3
1 and -3
What are the coordinates of the y-intercept?
(-3, 0)
(0, -3)
(2, 1)
y=-3
What is the significance of the ordered pair (2, -4) to the graph?
it is the vertex
it is the y-intercept
it is the axis of symmetry
it is the x-intercept
What is the equation for axis of symmetry?
y = 3
x = 3
x = 5
x = 1
Is the graph of the equation y=2x2 wider, narrower or the same width as the standard parabola y = x2?
wider
narrower
same
impossible to tell
Use the picture to find the vertex and axis of symmetry.
Vertex: (8, 3); axis of symmetry: y=3
Vertex: (8, 3); axis of symmetry: x=3
Vertex: (3, 8); axis of symmetry: y=3
Vertex: (3, 8); axis of symmetry: x=3
A parabola has a vertex at (-3,2).
What is the axis of symmetry?
y = -2
x = 3
x = -3
y = 2
Name the vertex
(1,1)
(0,0)
This is a _______________ function.
Linear
Exponential
Quadratic
Quadratic equations take the shape of a _______ when graphed.
parabola
straight line
snaked line
elliptical
f(x) = x2- 8x + 15.
The equation for the axis of symmetry line is
x=2a−btrue
false
Which letter determines if a parabola opens up or down?
a
h
k
Find the Axis of Symmetry of y=x2+12x−7
x = -6
x = 6
x = 12
x = -12
Find the Axis of Symmetry of y = - x2 - 14x - 59
x = 14
x = 7
x = -14
x = -7
Find the Axis of Symmetry of y = x2 - 12x + 46
x = 12
x = 6
x = -12
x = -6
y=4x2-8x+9
Find the Axis of Symmetry of
y = x2 - 6x + 11?
x = -3
x = -6
x = 6
x = 3
Find the axis of symmetry for y=x2−8x+15
x = -4
x = 4
y = 4
y = -4
Find the axis of symmetry of
y=3x2−6x+4
x=1
x=−6
x=2
x=−1
Determine the axis of symmetry for the function
f(x)=x2+4x+3x = -2
x = 2
x = -1.5
x = 4
Determine the axis of symmetry for the function
f(x)=x2−4x = 0
x = -2
x = 2
Cannot be determined
What is an equation of the axis of symmetry
of the parabola represented by y=2x2−3x+7? ?
x=43
y=43
x=23
y=23
Which equation represents the axis of symmetry of
the graph of the equation y = x2 + 4x - 5?
x = -4
x = -2
x = 4
x = 2
y=−x2+6x−4
What is an equation of the axis of symmetry
of the parabola represented by the equation above?
x = 3
y = 3
x = -3
y = -3
Which equation represents the axis of symmetry of
the graph of the equation y = x2 + 4x - 5?
x = -4
x = -2
x = 4
x = 2
What is the vertex of the equation
y=(x−3)2+5(-3, 5)
(3, 5)
(-3, -5)
(3, -5)
What is the vertex of the equation
y=(x+7)2+3(7, 3)
(7, -3)
(-7, 3)
(-7, -3)
What is the vertex of the equation
y=(x−4)2(-4, 0)
(4, 0)
(0, 4)
(0, -4)
What is the vertex of the equation
y=x2−1(0, -1)
(0, 1)
(1, 0)
(-1, 0)
What is the vertex of the equation
y=2(x+1)2−5(1, -5)
(-1, -5)
(-1, 5)
(1, 5)
What is the vertex of the equation
y=−2(x−1)2+5(-1, -5)
(-1, 5)
(1, 5)
(1, -5)
What is the vertex of the equation
f(x)=(x−4)2−5(-4, -5)
(-4, 5)
(4, 5)
(4, -5)
What direction does the following graph open?
f(x)=(x−4)2−5left
right
up
down
What is the vertex of the equation
g(x)=−x2+5(0, 5)
(0, -5)
(5, 0)
(-5, 0)
What direction does the following graph open?
g(x)=−x2+5right
left
down
up
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
y=a(x-h)2+k
What is the vertex of the equation
y=2(x+1)2−5(1, -5)
(-1, -5)
(-1, 5)
(1, 5)
What direction does the following graph open?
f(x)=(x−4)2−5left
right
up
down
f(x)=−(x−4)2+1
Choose the correct graph of the equation.
Which equation has a vertex of (5, −7)
y=2(x−5)2−7
y=(x−7)2−5
y=(x+5)2+7
y=2(x−1)2−4
Which equation has a vertex of (−3,−6)
y=2(x+3)2+6
y=(x+6)2+3
y=(x+12)2+16
y=2(x+3)2−6
What is the equation of this graph?
f(x)=(x+4)2+3
f(x)=(x+3)2−4
f(x)=(x−4)2−4
f(x)=(x−6)2−1
What is the equation of this graph?
(f(x)=(x+3)2−2
f(x)=(x+6)2−9
f(x)=(x+2)2+3
f(x)=(x−6)2−1
Given the equation
y=21(x−6)2+5
What is the X-value of the vertex?
21
5
−6
6
Given the equation
y=21(x+2)2−1
What is the Y-value of the vertex?
21
−2
1
−1
What is the vertex of the graph?
(4, 4)
(2, 2)
(0, 6)
(−2, 2)
IDENTIFY THE VERTEX AND AXIS OF SYMMETRY OF EACH
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What is the equation of the axis of symmetry?
x = 1
y = -4
y = 1
x = -4
Does this graph have a maximum or a minimum?
Both
Neither
Minimum
Maximum
What is the equation of the axis of symmetry for the parabola?
y = -1
x = -3
y = -3
x = -1
CHOOSE BEST ANSWER
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D
Given this directrix and vertex, what would the equation of the parabola be?
x=121(y−2)2+1
x=61(y−2)2+1
y=121(x−1)2+2
y=61(x−1)2+2
Write the equation of the parabola with vertex at the origin and a directrix at y=5.
x=−201y2
x=5y2
y=−201x2
y=−20x2
The directrix is a _______ that always lies ________ your parabola.
(a)
Write an equation of the parabola with the given characteristics:
Focus: (3, 5)
Vertex: (3, -1)
y = 241(x−3)2−1
y = −241(x+3)2−1
y = −241(x−3)2−1
Write an equation of the parabola with the given characteristics:
Opens Up
Vertex: (-2, 4)
1/16 unit away from the directrix
y =4(x+2)2−4
y =4(x+2)2+4
y =4(x−2)2+4
If a parabola has a focus at (0,3) and a vertex at the origin...what is the equation of the directrix?
y=3
y=-3
x=3
x=-3
If a parabola has a focus at (3,0) and a vertex at the origin...what is the equation of the directrix?
y=3
y=-3
x=3
x=-3
If a parabola has a focus at (-3,0) and a vertex at the origin...what is the equation of the directrix?
y=3
y=-3
x=3
x=-3
x=−81(y−4)2−1 What are the coordinates for the focus?
What is the directrix of the parabola y=81(x−4)2−3 ?
y=−3
x=5
y=−5
y=2
FIND THE FOCUS
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FIND THE DIRECTRIX
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FIND THE DIRECTRIX
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USE THE INFORMATION PROVIDED TO WRITE
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CHOOSE BEST ANSWERUSE THE INFORMATION PROVIDED TO WRITE
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CHOOSE BEST ANSWERUSE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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USE THE INFORMATION PROVIDED TO WRITE
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CHOOSE BEST ANSWERUSE THE INFORMATION PROVIDED TO WRITE
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CHOOSE BEST ANSWERUSE THE INFORMATION PROVIDED TO WRITE
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CHOOSE BEST ANSWERUSE THE INFORMATION PROVIDED TO WRITE
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f(x) = x2 + 12x - 2
written in vertex form?
f(x) = x2 - 8x + 1
written in vertex form?
x2-12x+40
into vertex form
y = x2 - 6x + 10?
Convert the equation y= x2 + 4x + 11 into vertex form.
y = (x + 2)2 - 4
y = (x + 2)2 + 7
y = (x + 2)2
y = (x - 2)2 - 7
Determine the vertex of the parabola y=5(x-2)2–7
(5, -7)
(-2, -7)
(2, -7)
(-7, -2)
) f (x) = 2x2 + 4x - 5
f (x) = 2(x + 1)2 - 7
f (x) = -2(x + 7)2 + 1
f (x) = 2(x - 9)2 + 3
f (x) = -2(x + 1)2 - 7
f (x) = 3x2 - 54x + 252
f (x) = 2(x - 9)2 + 9
f (x) = -3(x + 9)2 + 9
f (x) = -2(x - 9)2 + 9
f (x) = 3(x - 9)2 + 9
f (x) = 11x2 + 132x + 392
f (x) = 11(x + 6)2 + 4
f (x) = 11(x - 6)2 + 4
f (x) = 11(x + 6)2 - 4
f (x) = 11(x + 4)2 + 6
f (x) = 2x2 - 28x + 92
f (x) = 4(x - 7)2 + 6
f (x) = (x - 7)2 - 6
f (x) = 2(x - 7)2 - 6
f (x) = 2(x - 7)2 + 9
