(a) Sketch the graph of \(y = (x - 2)^2 - 3\). Show the coordinates of any turning points.
[3]
(b) The sketch shows part of a graph which has equation \(y = ax^2 + bx + c\).
Not to scale
Find the values of \(a\), \(b\) and \(c\). [5]
Mark scheme (a)
Answer
Marks
Part marks and guidance
U shaped parabola with minimum value indicated at (2, –3)
3
B1 for U shape curve
B1 for turning point at \((2, k)\) B1 for turning point at \((k, -3)\)
Be generous for the U shape condone broken line Values must be shown but could be marked on axes. Mark intention Accept turning point = (2, –3) written in working provided no contradiction on sketch If point (2, –3) only plotted on graph and no sketch then B0B1B1
Mark scheme (b)
Answer
Marks
Part marks and guidance
4, 16, 12
5
B4 for \(a = 4\) and \(b = 16\) OR B3 for \(c = 12\) and either \(a = 4\) or \(b = 16\) OR M1 for \((x + 3)(x + 1)\) seen isw A1 for \(x^2 + x + 3x + 3\) or better seen isw B1 for \(c = 12\)
OR B1 for \(c = 12\) soi
M1 for \((-1)^2a - 1b + 12 = 0\) oe and \((-3)^2a - 3b + 12 = 0\) oe
Alt method uses simultaneous equations with \(c = 12\) Allow recovery for omission of brackets if negatives correctly dealt with
