Given the curve $y = kx^2 + 2kx - 3$, where $k$ is a constant. By expressing $y$ in the f

Question

Given the curve $y = kx^2 + 2kx - 3$, where $k$ is a constant. By expressing $y$ in the form $k(x+b)^2 - 1$, determine the value of $k$ and of $b$.[3] Hence, show that the curve is always below the $x$-axis.[2] State the turning point of the curve and determine the nature of this point.[2]

Accepted Answer

(a) $k=-2$, $b=1$. (b) $y\leq-1<0$ for all real $x$, so the curve is always below the $x$-axis. (iii) $(-1,-1)$, maximum point.

2025 AHS PRELIMS P1 Q5

2025 AHS PRELIMS P1 Q5

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