JAMB 2017 · UTME · Q31

If the graphs $y = px^2 + q$ and $y = 2x^2 - 1$ intersect at $x = 2$ , find the value of $p$ in terms of $q$ .

Worked solution (try it first)

Find $y$ on the known curve at $x = 2$ : $y = 2(2)^2 - 1 = 7$ .
The other curve passes through the same point, so $p(2)^2 + q = 7$ , which is $4p + q = 7$ .
Subtract $q$ and divide by 4: $p = \dfrac{7 - q}{4}$ , option D.