3.39: Quadratic graph: coefficients and inequality

0606/21/M/J/23 — Question 3 · 5 marks

3.39 diagram
The diagram shows the graph of y=h(x)y = h(x) where h(x)=a(x+b)(cx+d)h(x) = a(x + b)(cx + d) and aa, bb, cc and dd are integers. The curve meets the xx-axis at (2,0)(-2, 0) and (1.5,0)(1.5, 0) and the yy-axis at (0,12)(0, 12).
(a)
Find the values of aa, bb and cc.
[2]
(b)
Use the graph to solve the inequality h(x)9h(x) \geqslant 9.
[3]