2. WMA11/01 Edexcel IAL P1 January 2022, Q2 (Quadratics: Completing The Square & Sketching)
(a) Express f(x) in the form
where a, b and c are integers to be found.
(3)
(b) Sketch the graph of the curve C with equation y = f(x), showing clearly the coordinates of the point where the curve crosses the y‑axis.
(2)
(c) Write down the equation of the line of symmetry of C.
(1)
SOLUTION
a- Using completing square method to express f(x) in the required form.
b-
Since this is a quadratic curve, the equation of a curve is represented in the form of a completed square/vertex form, y=a(x-p)2+q. The coordinates of a vertex point of the quadratic curve is (-1 , 13).
Whereas for finding x-intercept, put y=0 in f(x).
Whereas for finding y-intercept, put x=0 in f(x).
c-
Line of symmetry is a line, which passes through the centre of a graph and splits the graph into two identical parts.
In case of quadratic curves, always remember that the line of symmetry is a vertical line passing through the vertex point or turning point.
Hence, the equation of the line of symmetry is
