If a quadratic equation can be factorised, the factors can be used to find the roots of the equation. The equation factorises to give \((x + 3) (x - 2) = 0 \) so the solutions to the equation \(x^2 + ...

First we need to complete the square to get the coordinates of the turning point. \(y = {x^2} + 2x + 3\) \(y = {(x + 1)^2} - 1 + 3\) \(y = {(x + 1)^2} + 2\) Therefore ...