(a) (i) \(y = px^{2} - 5x + q\)

x	-3	-2	-1	0	1	2	3	4	5
y	21	6		-12				0	13

From the table,
y = -12 when x = 0, i.e. \(-12 = p(0^{2}) - 5(0) + q\)
\(q = -12\).
y = 0 when x = 4, i.e. \(0 = p(4^{2}) - 5(4) + q\)
\(0 = 16p - 20 + q \implies 20 = 16p + q .... (1) \)
Substitute q = -12 in (1),
\(20 = 16p - 12\)
\(20 + 12 = 16p \implies p = \frac{32}{16} = 2\)
Equation : \(y = 2x^{2} - 5x - 12 \).
(ii) Given the equation \(y = 2x^{2} - 5x - 12\). The table becomes

x	-3	-2	-1	0	1	2	3	4	5
y	21	6	-5	-12	-15	-14	-9	0	13

(b)
(c) From the graph,
(i) When x = 1.8, y = -14.5 ; (ii) When y = -8, x = -0.65 or 3.15 or 3.2.