Given: *f(x)* = -x^{2} + 6x + 7

5.1 Determine the coordinates of the turning point of* f*. (3)

5.2 Determine the *x*-intercepts of *f*. (2)

5.3 Draw a neat sketch of *f*, clearly indicating all intercepts with the axes and the turning

point. (4)

5.4 Write down the equation of the axis of symmetry of *f*. (1)

5.5 Determine the average gradient of f between *x* = -3 and* x* =1. (4)

5.6 The graph of f is shifted 4 units to the left and reflected in the *x*-axis to form *h*.

Write down the equation of *h* in the form* h(x)* = *a*(x + *p*)^{2} +*q*. (2)

**[16]**