The sketch below shows the graph of the function *f(𝑥)* = *a𝑥 ^{2} + b𝑥 +c.*

The straight line with equation *3y = 𝑥 – 5* intersects *f* at *B*. The points *A(-2;0) *and *B* are the *𝑥*-intercepts of *f* . Point *D*(-1;3)is a point on *f* .

9.1 Determine the coordinates of *B*.(2)

9.2 Determine the equation of *f* .(4)

9.3 Determine the coordinates of the turning point of *f* .(2)

9.4 Point *E* is a point on the straight line so that *DE* is parallel to the *y*-axis. Determine the length of *DE*.(3)

9.5 Calculate the average gradient between *B* and *D*.(1)

9.6 For which value(s) of *𝑥* is *𝑥* x *f* (𝑥) ≥ 0?(2)

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