Quick questions on Graphical solution of equations explained: O-Level E-Maths

The solutions (roots) of $f(x) = 0$ are the values of $x$ where the graph of $y = f(x)$ crosses the $x$-axis, because there $y = 0$. Reading these crossing points off a carefully drawn curve gives the solutions to the accuracy of the graph.

To solve an equation of the form $f(x) = g(x)$, draw $y = f(x)$ and $y = g(x)$ on the same axes. The solutions are the $x$-coordinates of the points where the two graphs intersect, since there the two expressions are equal.

The gradient of a curve at a point changes from place to place. To estimate it, draw a tangent (a straight line just touching the curve at that point), pick two clear points on the tangent, and compute its gradient as rise over run. The tangent's gradient is the curve's gradient there.

The graph of $y = x^2 - 4$ is drawn. State how to read off the solutions of $x^2 - 4 = 0$. [1 mark]

To solve $x^2 = 3x$ using the curve $y = x^2$, what line should you draw? [1 mark]

A tangent to a curve passes through $(1, 2)$ and $(3, 8)$. Estimate the gradient of the curve where the tangent touches. [2 marks]