JAMB 2016 · UTME · Q9✱✱

The gradient of a curve is $2x + 7$ and the curve passes through the point $(2, 0)$ . Find the equation of the curve.

Worked solution (try it first)

Integrate the gradient to get the curve: $y = x^2 + 7x + c$ .
The curve passes through $(2, 0)$ , so put in $x = 2$ and $y = 0$ : $0 = 4 + 14 + c$ .
So $c = -18$ and the curve is $y = x^2 + 7x - 18$ , option B.