Definition: Quadratic function-A function f is a quadratic
function if

where a, b, and c are real numbers and a is not 0.

The graph is a **parabola.
**

Parabolas are

1. Symmetric about a line (line of symmetry is called the axis)

2. The maximum or minimum point on the curve is called the vertex

Standard curve: f(x)=x

Graphs to be compared to the standard curve:

General Principles for Graphs for Quadratic Functions

1. The graph of the quadratic function defined by

where (h,k) are coordinates of the vertex.

2. The graph opens upward if a is positive and downward if a is negative.

3. The graph is wider than that of The graph
is narrower than that of

Steps in graphing a parabola:

1. Find the vertex. Find the vertex either by using the formula or by completing
the

square.

2. Select two x coordinates to the left of the vertex and two corresponding
points to

the right of the vertex.

3. Calculate the y coordinates.

4. Plot the points.

Graph the following by selecting at least five points.

Word Problem

1. Ruth Tynes has 40 yards of fence to enclose a rectangular garden. Find the

dimensions of the rectangle that will give maximum area.

2. A projectile on Earth is fired straight upward so that its distance (in feet)
above

the ground t seconds after firing is given by

Find the maximum height it reaches and the number of
seconds it takes to reach

that height.