The are four points that suffice to sketch any quadratic curve:

1. the maximum or minimum

2. The intersection with the – axis

3. The intersections, if any with the– axis. In general a quadratic curve may meet the– axis at 0, 1 or 2 points.

Given the quadraticwe find these points in the following way.

1. Complete the square. In the formThe minimum is atifand the maximum is atif

2. The intersection with the– axis is found by substitutinginto the equation for

3. The intersections with the– axis, if any are found by solvingeither by factorising or using the quadratic formula.

Example:The completed square form isFollowing steps 1, 2 and 3 above gives a minimum atan intersection with the– axis atand intersections with the– axis atandWe can sketch the curve.

Example:The completed square form isFollowing steps 1, 2 , 3 above gives a maximum atan intersection with the– axis atand intersections with the x – axis at (-1,0) andWe can sketch the curve.