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Graphing Quadratic Functions

Graphing Quadratic Functions

It can open up with
the vertex being a
minimum
← The vertex is
the turning point

 

←The vertex is
the turning point.
Or it can open down
with the vertex
being a maximum

Finding the vertex is necessary to graph t he parabola and for answering any
questions regarding maximums and minimums.

The two formats that we use for quadratic functions are listed be low .

General: y or where the vertex is (h,k )
or
Standard y or f (x) = ax2+ bx + c where the vertex can be found by the
formula
and y is found by plugging the x into the function.

ln either format the" a" is the same value. lf a is positive , the parabola opens u p
and if it is negative , the parabola opens down.

To Graph a Parabola:

1. Find and plot the vertex

2. Pick two x values smaller (or larger) than the x - coordinate of the vertex .
Find the y -values and plot the points.

3. Draw your line of symmetry locate the image of the points from step 2
on the other side of the line of symmetry .

4. Draw the parabola.

On problems where you are asked to maximize or minimize a value you will find
the vertex of the parabola. The maximum or minimum is the" y"-coordinate and
it occurs at the "x"-coordinate.

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