Express $y = 4x - 4x^2 - 3$ in the form $p(x + q)^2 + r$ where $p$, $q$ and $r$ are c

Question

Express $y = 4x - 4x^2 - 3$ in the form $p(x + q)^2 + r$ where $p$, $q$ and $r$ are constants.[2] Hence, explain whether $4x - 4x^2 - 3 = 0$ has any real solutions.[2]

Accepted Answer

(a) $y=-4(x-\frac{1}{2})^2-2$ (b) No real solutions.

2025 PHS PRELIMS P1 Q6

2025 PHS PRELIMS P1 Q6

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