Additional Mathematics 4037: Quadratic functions Topical Past Paper Questions

**(a)** > **(i)** Write $x^2 - x - 6$ in the form $(x + a)^2 + b$ where $a$ and $b$ are constants. [2] > > **(ii)** Hence write down the coordinates of the stationary point on the curve $y = x^2 - x - 6$. [2] **(b)** On the axes, draw the graph of $y = |x^2 - x - 6|$ for $-4 \leq…

DO NOT USE A CALCULATOR IN THIS QUESTION. Write $ \frac{16+11\sqrt{10}}{2+\sqrt{10}}+1 $ in the form $ p+q\sqrt{10} $, where p and q are integers. $$ \left\| \mathbf{4} \right\| \left\| \mathbf{4} \right\| $$

Find the values of $k$ for which the curve $y = x^{2} + kx + (4k - 15)$ is completely above the $x$-axis. [4]