Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

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

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

(ii)[1]

State the range attained by $f$.

(iii)[1]

The function $g$ is specified by $g : x \mapsto 2x^2 - 12x + 7$ for $x \leq k$. State the largest value of $k$ for which $g$ has an inverse.

(iv)[3]

Given that $g$ has an inverse, find an explicit expression for $g^{-1}(x)$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: The completed square is $2(x-3)^2-11$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI