Using only this information, write down an equation in terms of a and b.

Using this information, write down a second equation in terms of a and b.

Hence find the value of a and of b.

The graph intersects the x-axis at a second point, P.

Find the x-coordinate of P.

$1.75 = \frac{{ - b}}{{2a}}$ (or equivalent)      (A1) (C1)

Note: Award (A1) for $f\left( x \right) = {\left( {1.75} \right)^2}a + 1.75b$ or for $y = {\left( {1.75} \right)^2}a + 1.75b + 22$ or for $f\left( {1.75} \right) = {\left( {1.75} \right)^2}a + 1.75b + 22$.

[1 mark]

${\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0$ (or equivalent)      (A1) (C1)

Note: Award (A1) for ${\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0$ seen.

Award (A0) for $y = {\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22$.

[1 mark]

a = −2, b = 7     (A1)(ft)(A1)(ft) (C2)

Note: Follow through from parts (a) and (b).
Accept answers(s) embedded as a coordinate pair.

[2 marks]

−2x² + 7x + 22 = 0     (M1)

Note: Award (M1) for correct substitution of a and b into equation and setting to zero. Follow through from part (c).

(x =) 5.5     (A1)(ft) (C2)

Note: Follow through from parts (a) and (b).

OR

x-coordinate = 1.75 + (1.75 − (−2))     (M1)

Note: Award (M1) for correct use of axis of symmetry and given intercept.

(x =) 5.5     (A1) (C2)

[2 marks]