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Quadratic Graphs

Quadratic Graphs

A quadratic function will contain a squared term, but will have no higher power. Plotted on a graph, it will be in the shape of a parabola, which is a curve that comes to a rounded point then turns to curve back again.

The point at which it turns is a turning point, and this will be either a minimum or a maximum value. Curves can fall, turn, and rise again; or they may rise, peak, and fall.

Draw graphs as accurately to obtain any turning points or roots.

Example 1

Plot the graph `y = x^2 - 3`.

The graph y = x2 - 3 may be plotted using the following points:

`x` -4 -3 -2 -1 0 1 2 3 4
`x^2 - 3` 13 6 1 -2 -3 -2 1 6 13


Graph of f(x)=x<sup>2-3

Example 2

For the graph, above: is the turning point a minimum value or a maximum value?

The point at which the graph turns is the lowest point for the line. It is therefore a minimum point.

Answer: Minimum

See also Solving Quadratic Equations using a Graph