Question 6

The diagram below shows the graphs of f(x)=-x2 + 2x+15 and g(x)=-3x+k. Graph f cuts the x-axis at A(-3 ; 0) and B(5 ; 0), the y-axis at C and has a turning point at D. Graph g cuts the x-axis at B and the y-axis at C. E is a point on g such DE is

parallel to the y-axis.

6.1 Show that k = 15 (1)

6.2 Determine the coordinates of D, the turning point of f. (3)

6.3 Determine the values of x for which f is increasing. (1)

6.4 Calculate the average gradient between points A and D. (3)

6.5 Calculate the length of DE. (2)

6.6 If h(x) = f(x-1)-2, determine the equation of h in the form h(x) = a(x + p)2 + q. (4)

6.7 Determine the maximum value of p(x) = 3f(x)-12 (3)

6.8 Determine the values of x for which f(x) + k = 0 will have two distinct real roots. (2)


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