JAMB 1983 · UME · Q18

Which of the following equations represents the graph shown?

The vertical scale is a quarter of the horizontal scale.

Worked solution (try it first)

The curve opens downward, so the $x^2$ term is negative.
That leaves options C and D, which both cut the $y$ -axis at 1.
The curve crosses the $x$ -axis at $-1$ and $\frac13$ , so the factors are $(1 + x)$ and $(1 - 3x)$ .
Expand: $(1 + x)(1 - 3x) = 1 - 3x + x - 3x^2$ , which is $1 - 2x - 3x^2$ .
So the graph is $y = 1 - 2x - 3x^2$ , option D.