WorkSHEET 9.1
Quadratic graphs
Name: ___________________________
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1
Plot the graph of y = x2 for values of x from
−3 to 3 inclusive. State the equation of the axis
of symmetry and the coordinates of the turning
point.
2
Plot the graph of y = −x2 for values of x from
−3 to 3 inclusive. State the equation of the axis
of symmetry and the coordinates of the turning
point.
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3
Plot the graph of y = x2 – 1 for values of x from
−3 to 3 inclusive. State the equation of the axis
of symmetry and the coordinates of the turning
point.
4
Plot the graph of y = (x – 1)2 for values of
x from −3 to 3 inclusive. State the equation of
the axis of symmetry and the coordinates of the
turning point.
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5
Plot the graph of y = (x + 1)2  1 for values of
x from −3 to 3 inclusive. State the equation of
the axis of symmetry and the coordinates of the
turning point.
6
For the equation y = x2 + 2:
(a) state the vertical translation
(b) state the coordinates of the turning point
(c) sketch the curve.
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7
For the equation y = (x + 2)2:
(a) state the horizontal translation
(b) state the coordinates of the turning point
(c) sketch the curve.
8
Sketch the graph of the following quadratic
equations:
(a) y = 2x2
(b)
y=
1 2
x
2
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9
On the same set of axes, sketch the graphs of
the quadratic equations y = x2 and y = −x2.
10
Sketch each of the following quadratic
equations:
(a) y = −(x – 2)2
(b)
y = 2 – x2
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1
For each of the following graphs, state the
coordinates of the turning point and whether it
is a maximum or a minimum:
(a) y = (x + 3)2  7
(b)
2
For each of the following graphs, state the
coordinates of the turning point, whether it is a
maximum or a minimum, and whether it is
narrower or wider than y = x2.
(a) y = 0.2(x – 5)2  4
(b)
3
y = −(x – 4)2 + 2
y = −6(x + 4)2 + 9
Describe the translations required to change
y = x2 into:
(a) y = (x – 7)2 + 6
(b)
y = (x + 8)2 – 9
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4
State the equation of each of the following:
(a)
(b)
5
For the equation y = (x – 2)2 + 5:
(a) state the coordinates of the turning point
(b)
state whether it is a maximum or
minimum
(c)
state the y-intercept
(d)
state if it is wider or narrower than y = x2
(e)
sketch the curve.
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6
7
For the equation y = −(x + 1)2 – 4:
(a) state the coordinates of the turning point
(b)
state whether it is a maximum or
minimum
(c)
state the y-intercept
(d)
state if it is wider or narrower than y = x2
(e)
sketch the curve.
For the equation y = 2(x  1)2 – 3:
(a) state the coordinates of the turning point
(b)
state whether it is a maximum or
minimum
(c)
state the y-intercept
(d)
state if it is wider or narrower than y = x2
(e)
sketch the curve.
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8
Complete the square on each of the following
to find the equation, and therefore the
coordinates of the turning point:
(a ) y  2 x 2  10 x  9
(b)
y  3x 2  11x  1
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9
Sketch the graph of y = x2 + 4x + 9 using the
completing the square method to find the
coordinates of the turning point.
10
Sketch the graph of y  x 2  6 x  7 using the
x-intercepts to find the coordinates of the
turning point.
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