More worked examples involving quadratics

Finding the vertex from the equation (click to enlarge):

Factorising where a>1 using the box method (click to enlarge):

Note: To use the box method you must have factored out all obvious common factors first. E.g. To factorise 6x² – 8x – 8 using the box method, you must first factorise out the obvious factor of 2 so that it becomes 2(3x² – 4x – 4)