# Quadratic Functions and Models

**Basic Forms of a Quadratic Function **

There are two basic forms for quadratic functions. The first one (standard form)
is f (x) = ax^{2} + bx + c

and the second one ( vertex form ) is f (x) = a(x - h) ^{2} + k . The graph of a
quadratic function is a

parabola . If a is positive , the parabola opens upward and if a is negative, it
opens downward.

Example: Consider the following quadratic function . Find
the maximum or minimum function value ,

the axis of symmetry, and the range:

** Finding the Vertex
**

Given the vertex form of a quadratic function, the vertex is the point (h, k ) . Given the standard form of a

quadratic function , the x coordinate of the vertex is given by

Example: Find the vertex .

** Additional Notes **

• In exercises # 103 & 105, you are asked to use least -squares

regression to find a quadratic function that

models the data. This is done almost in exactly the same way that linear
regression is done.

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