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In previous math courses, you learned that a quadratic function defined by an equation of the form y = a(x - p)2 + q or y = ax2 + bx + c represents a shape called a parabola.

Note that you can switch from the form y = ax2 + bx + c to the more useful equation y = a(x - p)2 + q by using the method of completing the square which you reviewed on page 1 of this section.

Let's review how to sketch the graph of a parabola given an equation of the form y = a(x - p)2 + q.

In order to sketch the graph of a parabola given its equation, it is useful to find a few points which satisfy the equation, plot them on a coordinate plane, and then draw a parabola passing through these points.

Let's begin by sketching the most basic parabola y = x2.

x	y = x2
	0	0
	1	1
	-1	1
	2	4
	-2	4
	5	25
	-5	25

We can easily see that this parabola, defined by the equation y = x2, opens upward and is centred at (0, 0).

Now look at a more involved equation y = (1/4)(x - 6)2 + 3. to practice graphing parabolas and noticing the translation effect.

From this example, do you think you can summarize the effects of a, p and q in the parabola equation y = a(x - p)2 + q?

If not, look at a summary and questions that cover all you need to know in order to sketch parabolas.