Equations of curves - Intermediate & Higher tier – WJECSolving quadratic equations graphically - Higher

If we want to solve the equation \(\text{x}^2+\text{x}-\text{2 = 0}\), we need to look at the graph of \(\text{y = x}^2+\text{x}-\text{2}\).

The solutions to the equation are the points where \(\text{y = 0}\), ie where the graph crosses the \({x}\)-axis.

The graph crosses the \({x}\)-axis at \(\text{x = -2}\) and \(\text{x = 1}\), so these are the solutions to the equation \(\text{x}^2+\text{x}-\text{2 = 0}\).

If instead we want to solve \(\text{x}^2+\text{x}-\text{2 = 10}\), we need to look at the points where \(\text{y = 10}\).

To do this, we can draw the line \(\text{y = 10}\) on the graph. The solutions are where the curve crosses this line.

The curve crosses the line at the points \(\text{x = -4}\) and \(\text{x = 3}\) so these are the solutions to the equation \(\text{x}^2+\text{x}-\text{2 = 10}\).