(a)[2]
With a scale of $2\text{ cm}$ to $1$ unit on the $x$-axis for $-3 \le x \le 2$ and a scale of $1\text{ cm}$ to $1$ unit on the $y$-axis for $-4 \le y \le 4$, plot the points from the table and connect them with a smooth curve.
(b(i))[1]
Use your graph to estimate the roots of the equation $x^2 + x - 3 = 0$.
(b(ii))[2]
Use your graph to estimate the roots of the equation $x^2 + x - 5 = 0$.
(c)[2]
Estimate the gradient of the curve at $(1, -1)$ by drawing a tangent.
(d(i))[2]
The equation $x^2 - x - 1 = 0$ may be solved by adding a straight line to the graph of $y = x^2 + x - 3$. Determine the equation of that straight line.
(d(ii))[2]
Draw the straight line and hence solve $x^2 - x - 1 = 0$.