The curve C has equation .
Find the coordinates of any points where C intersects the coordinate axes.
Sketch the graph of C, showing clearly all points of intersection with the coordinate axes.
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The curve C has equation .
Find the coordinates of any points where C intersects the coordinate axes.
Sketch the graph of C, showing clearly all points of intersection with the coordinate axes.
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Write the quadratic function in the form where a, b and c are integers to be found.
Write down the minimum point on the graph of .
Sketch the graph of , clearly labelling the minimum point and any point where the graph intersects the coordinate axes.
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Solve the equation .
Find the coordinates of the turning point on the graph of .
Sketch the graph of , labelling the turning point and any points where the graph crosses the coordinate axes.
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Find the minimum value of the function .
Hence, or otherwise, prove that the function has no real roots.
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The function has two distinct real roots.
Show that .
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The equation has real roots.
Find the possible values of k.
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The equation has no real roots. Show that .
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The graph below shows the curve .
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.
Write down the maximum height of the bridge above the water.
Is the bridge wide enough to span a river of width 11 m?
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The diagram below shows the graph of , where is a quadratic function.
The intercepts with the x-axis and the turning point have been labelled.
Write down the equation of the axis of symmetry for the graph of
The function can be written in the form of
Find the values of and .
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Solve the equation .
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Solve .
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Let , for where .
Show that the discriminant of f is .
Find the values of so that the function f(x) has two distinct roots.
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