## Sketching Quadratic Curves

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 quadratic we find these points in the following way.

1. Complete the square. In the form The minimum is at if and the maximum is at if 2. The intersection with the – axis is found by substituting into the equation for 3. The intersections with the – axis, if any are found by solving either by factorising or using the quadratic formula.

Example: The completed square form is Following steps 1, 2 and 3 above gives a minimum at an intersection with the – axis at and intersections with the – axis at and We can sketch the curve. Example: The completed square form is Following steps 1, 2 , 3 above gives a maximum at an intersection with the – axis at and intersections with the x – axis at (-1,0) and We can sketch the curve.  