Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

The curve with $\frac{dy}{dx} = 7 - x^2 - 6x$ goes through $(3, -10)$.
(i)[3]

Find the equation that represents the curve.

(ii)[2]

Write $7 - x^2 - 6x$ in the form $a - (x + b)^2$, where $a$ and $b$ are constants.

(iii)[3]

Find the values of $x$ for which the gradient of the curve is positive.

(c(ii))[2]

Write $7 - x^2 - 6x$ in the form $a - (x + b)^2$, where $a$ and $b$ are constants.

(c(iii))[3]

Find the values of $x$ for which the gradient of the curve is positive.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Integrate to obtain $y=7x-\dfrac{x^3}{3}-\dfrac{6x^2}{2}+c$

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