Solve x^2 - 3x - 10 = 0 for x by a) factorising and b) the quadratic equation. Then draw a graph of the function, marking when it touches each of the axes.

a) We factorise to find 2 numbers a and b in (x + a)(x + b) such that a + b = -3 and whose product is -10 (ab = -10). (x + 2)(x - 5) = 0 -> x = 5 or -2b) This is a direct application of the quadratic formula, as provided in GCSE formula books. (-b +/- root(b^2 - 4ac))/2a. So, with a = 1, b = -3 and c = -10 -> x = 5 or -2c) Student should draw a smooth graph intersecting the x axis at 5 and -2, the y axis at -10 (subbing in x = 0) and whose minimum is in lower right quadrant (from the fact that the graph of x^2 is symmetrical, not expected to know differentiation).