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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 = 2

1x

2

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9 On the same set of axes, sketch the graphs of

the quadratic equations y = x2 and y = −x

2.

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) y = −(x – 4)2 + 2

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) y = −6(x + 4)2 + 9

3 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 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.

7 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:

9102)a( 2 xxy

1113)b( 2 xxy

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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 762 xxy using the

x-intercepts to find the coordinates of the

turning point.