(a) Find the value of p and the value of q.
(b) Calculate the discriminant of 4x – 5 – x2
(c) On the axes on page 17, sketch the curve with equation y = 4x – 5 – x2 showing clearly the coordinates of any points where the curve crosses the coordinate axes.
(a) Find the value of the constant p.
The line L2 passes through the point C (2, 4) and is perpendicular to L1
(b) Find an equation for L2 giving your answer in the form ax + by + c = 0, where a, b and c are integers.
(c) Find the coordinates of the point D.
(e) Find the area of the quadrilateral ACBE.
There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point A.
(a) Write down the coordinates of the point A.
(b) On separate diagrams sketch the curve with equation
(i) y = f(x + 3)
(ii) y = f(3x)
On each sketch you should indicate clearly the coordinates of the maximum point and any points where the curves cross or meet the coordinate axes.
The curve with equation y = f (x) + k, where k is a constant, has a maximum point at (3, 10).
(c) Write down the value of k.
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