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(xh)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)=x2 using transformations.

We get the graph of f(x)=a(xh)2+k from the graph of f(x)=x2 as follows:

f(x)=x2f(x)=ax2Vertical stretching or shrinking with a reflectionacross the x-axis if a<0f(x)=a(xh)2Horizontal translationf(x)=a(xh)

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