(a) The roots of the equation are -1.5 or 2. (b) C = 6 (intercept on the positive vertical axis) \(ax^{2} + bx + c = 0\) When x = 2, c = 6 \(4a + 2b + 6 = 0 \implies 4a + 2b = -6 ....(1)\) When x = -1.5, c = 6 \(a(-1.5)^{2} + b(-1.5) = -6\) \(\frac{9a}{4} - \frac{3b}{2} = -6 \implies 9a - 6b = -24 ... (2)\) Multiply (1) by 3 : \(12a + 6b = -18 ... (1a)\) (1a) + (2) : \(12a + 9a = -18 - 24 \implies 21a = -42\) \(a = -2\) \(4a + 2b = -6 \implies 4(-2) + 2b = -6\) \(2b = -6 + 8 = 2 \implies b = 1\) (a, b, c) = (-2, 1, 6) Hence the relation illustrated in the graph is \(y = -2x^{2} + x + 6\). (c) When \(x = 0.2, y_{max} = 6.2\) (d) When \(y = 2, x = \text{ -1.2 or 1.7}\)