Irina uses a set of coordinate axes to draw her design of a window. The base of the window is on the x-axis, the upper part of the window is in the form of a quadratic curve and the sides are vertical lines, as shown on the diagram. The curve has end points (0,10) and (8,10) and its vertex is (4,12). Distances are measured in centimetres. The quadratic curve can be expressed in the form y = ax^2 + bx + c for 0 ≤ x ≤ 8.

$(c=) 10$ A1

$64a+8b+10=10$ A1 $16a+4b+10=12$ A1 Note: Award A1 for each equivalent expression or A1 for the use of the axis of symmetry formula to find $4=\frac{-b}{2a}$ or from use of derivative. Award A0A1 for $64a+8b+c=10$ and $16a+4b+c=12$.

$y=-\frac{1}{8}x^2+x+10$ A1A1 Note: Award A1A0 if one term is incorrect, A0A0 if two or more terms are incorrect. Award at most A1A0 if correct $a$, $b$ and $c$ values are seen but answer not expressed as an equation.