The are four points that suffice to sketch any quadratic curve:
-
the maximum or minimum
-
The intersection with the
– axis
-
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.
-
Complete the square. In the form
The minimum is at
if
and the maximum is at
if
-
The intersection with the
– axis is found by substituting
into the equation for
-
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.