Sketching Quadratic Curves
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.