Sketch the inequality x^2 - x - 12 > y on a set of axes.
First thing to note: this is a sketch question, and we're asked to sketch a quadratic (because there's an x2 term). So we need to factorise (put the brackets in) to work out where it crosses the x-axis. The trick is to find two numbers which multiply to make the last number (-12) and add to make the middle number (-1). After some thinking, this is 3 and -4.So we can write the quadratic as (x+3)(x-4). Along the x-axis, this equals zero. If two brackets multiply to make zero, then one of those brackets must have been zero. So the graph crosses at x=-3 and x=4. Now, we draw the usual quadratic shape, and shade below the curve.
