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Quadratic Functions and Applications

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)=x2

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

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.