# 3.3 Analyzing Graphs of Quadratic Functions

Find the vertex, the axis of symmetry, and the maximum or minimum value of a quadratic function using the method of completing the square.

Graph quadratic functions.

Solve applied problems involving maximum and minimum function values.

# Graphing Quadratic Functions of the Type $f(x)=a{(x-h)}^{2}+k$

The graph of a quadratic function is called a **parabola**. The graph of every parabola evolves from the graph of the squaring function $f(x)={x}^{2}$ using transformations.

We get the graph of $f(x)=a{(x-h)}^{2}+k$ from the graph of $f(x)={x}^{2}$ as follows:

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