Math 160 Notes Packet #6 Quadratic Functions - Prof. Beydler

Notes Packet #6

Math 160 – Prof. Beydler

Page 1 of 6

Quadratic Functions

(covers parts of Sullivan 3.3 and 3.4)

A _______________________ is a function that can be written in the form:

�� ( �� ) = ��

+ �� + ��

(where �� ≠ 0)

The graph of any quadratic function is a parabola.

Often, it is useful to write quadratic functions in standard form:

�� ( �� ) = �� ( �� − ℎ )

+ ��

It’s useful because we can easily identify the parabola’s vertex (ℎ, ��).

For both forms above, if �� > 0 then the parabola opens ____, and if

�� < 0 then the parabola opens ______.

Ex 1.

Let �� ( �� ) = 3��

+ 6�� + 5. Express �� in standard form (by completing the square).

What is the vertex of ��? __________

Sketch the graph of ��.

What is the minimum value of ��? _______

What is the range of ��? ___________

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