DP IB Maths: AA SL

Topic Questions

2.2 Quadratic Functions & Graphs

1a
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3 marks

The curve C has equation y equals x squared minus 3 x plus 2.

Find the coordinates of any points where C intersects the coordinate axes.

1b
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3 marks

Sketch the graph of C, showing clearly all points of intersection with the coordinate axes.

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2a
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2 marks

Write the quadratic function y equals x squared plus 8 x minus 9  in the form y equals a left parenthesis x plus b right parenthesis squared plus c where a, b and c are integers to be found.

2b
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1 mark

Write down the minimum point on the graph of y equals x squared plus 8 x minus 9.

2c
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3 marks

Sketch the graph of y equals x squared plus 8 x minus 9, clearly labelling the minimum point and any point where the graph intersects the coordinate axes.

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3a
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2 marks

Solve the equation 2 x squared plus x minus 6 equals 0.

3b
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3 marks

Find the coordinates of the turning point on the graph of y equals 2 x squared plus x minus 6.

3c
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2 marks

Sketch the graph of y equals 2 x squared plus x minus 6, labelling the turning point and any points where the graph crosses the coordinate axes.

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4a
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3 marks

Find the minimum value of the function straight f left parenthesis x right parenthesis equals x squared plus 4 x plus 5.

4b
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2 marks

Hence, or otherwise, prove that the function straight f left parenthesis x right parenthesis equals x squared plus 4 x plus 5 has no real roots.

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5
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3 marks

The function straight f left parenthesis x right parenthesis equals k x squared plus 2 k x minus 3 has two distinct real roots.

Show that k less than negative 3 space or space k greater than 0.

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6
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3 marks

The equation 2 x squared minus 4 x plus 3 minus 2 k equals 0 has real roots.

Find the possible values of k.

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7
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2 marks

The equation y equals x squared plus p x plus q has no real roots. Show that p squared less than 4 q.

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8a
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1 mark

The graph below shows the curve straight f left parenthesis x right parenthesis equals 4 minus x squared over 8.

The curve is to be used as the model for the arch on a bridge where the water level under the bridge is represented by the x-axis. All measurements are in meters.

2-2-edexcel-alevel-maths-pure-q8medium

Write down the maximum height of the bridge above the water.

8b
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3 marks

Is the bridge wide enough to span a river of width 11 m?

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9a
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1 mark

The diagram below shows the graph of y equals straight f left parenthesis x right parenthesis, where straight f left parenthesis x right parenthesis is a quadratic function.
The intercepts with the x-axis and the turning point have been labelled.

2-2-edexcel-alevel-maths-pure-q9medium

Write down the equation of the axis of symmetry for the graph of y equals space straight f left parenthesis x right parenthesis.

9b
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3 marks

The function straight f left parenthesis x right parenthesis spacecan be written in the form of straight f left parenthesis x right parenthesis equals a left parenthesis x minus h right parenthesis squared plus k.
Find the values of a comma space h and k.

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10
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3 marks

Solve the equation x to the power of 4 minus 13 x squared plus 36 equals 0.

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11
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4 marks

Solve x to the power of 2 over 5 end exponent plus x to the power of 1 fifth end exponent equals 6.

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12a
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3 marks

Let straight f left parenthesis x right parenthesis equals 2 p x squared plus left parenthesis 2 p minus 5 right parenthesis x plus p minus 5 over 2 comma, for x space element of space straight real numbers  where p space element of space straight rational numbers .

Show that the discriminant of f is negative 4 p squared plus 25.

12b
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3 marks

Find the values of p so that the function f(x) has two distinct roots.

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