Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

The function $f$ is defined as $f : x \mapsto 7 - 2x^2 - 12x$ for $x \in \mathbb{R}$.
(i)[2]

Express $7 - 2x^2 - 12x$ in the form $a - 2(x + b)^2$, with $a$ and $b$ as constants.

(ii)[1]

State the coordinates of the stationary point that lies on the curve $y = f(x)$.

(iii)[1]

The function $g$ is defined by $g : x \mapsto 7 - 2x^2 - 12x$ for $x \geq k$. State the least value of $k$ that allows $g$ to have an inverse.

(iv)[3]

For this value of $k$, determine $g^{-1}(x)$.

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