In both forms the highest exponent of x is 2.
The vertex, stationary point or turning point gives either the maximum or minimum value of the function.
Method 1: Factorisation.
If the equation is in the form y = ax2 + bx + c the following method should be used:
Step (a) Factorise the function. Step (b) Find the x- and y-intercepts by putting y = 0 and x = 0. Step (c) Find the axis of symmetry − always midway between the two x-intercepts. Step (d) Find the coordinates of the vertex or turning point. Example
Method 2: Transformation.
This method finds the coordinates of the vertex.
The y-intercept is found by putting x = 0.
The graph of the basic parabola y = x2 is shown in the diagram.
This basic parabola is moved or transformed as follows:
(a) y = ax 2 The a has the effect of changing the
parabola in the y- direction.
It affects the steepness of the graph.
(b) y = x 2 + k
The k has the effect of moving the parabola along the y-axis by k units.
(c) y = (x − h)2
The h has the effect of moving the basic parabola along the x-axis by h units.
Download an interactive spreadsheet (Microsoft Excel) showing the transformation of parabolas.
(Windows users, right click and "Save target as..." to save the files on your computer.)
If the function does not factorise, either complete the square (example), or use the quadratic formula.
If the function has no roots, i.e. It does not factorise and the quadratic formula cannot be used (the discriminant is negative) then some points have to be plotted.