The equation of a curve is $y = px^2 - (p + 2)x + 1$, where $p$ is a constant. Given that&n

Question

The equation of a curve is $y = px^2 - (p + 2)x + 1$, where $p$ is a constant. Given that $p > 0$, by completing the square, find the minimum value of $y$. Express your answer in the form $\frac{a - p^2}{bp}$, where $a$ and $b$ are integers.[3] Given instead that $p < 0$, find the coordinates of the maximum point in terms of $p$.[2]

Accepted Answer

(a) $\dfrac{-p^2-4}{4p}$, where $a=-4$ and $b=4$ (b) $\left(\dfrac{p+2}{2p},\dfrac{-p^2-4}{4p}\right)$

(A Math) 2025 CCHY PRELIMS P2 Q2

(A Math) 2025 CCHY PRELIMS P2 Q2

Solution:

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