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) = ax^{2}+ 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.