9-1 Quadratic Graphs and Their Properties

Objective

To graph quadratic functions of the form y = a x 2 y equals , eh x squared  and y = a x 2 + c y equals , eh x squared , plus c

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Recall from Chapter 8 that a polynomial of degree 2, such as − 16 x 2 + 64 , negative , 16 x squared , plus 64 comma  is called a quadratic polynomial. You can use a quadratic polynomial to define a quadratic function like the one in the Solve It.

Essential Understanding A quadratic function is a type of nonlinear function that models certain situations where the rate of change is not constant. The graph of a quadratic function is a symmetric curve with a highest or lowest point corresponding to a maximum or minimum value.

The simplest quadratic function f ( x ) = x 2 f open x close equals , x squared  or y = x 2 y equals , x squared  is the quadratic parent function.

The graph of a quadratic function is a U-shaped curve called a parabola. The parabola with equation y = x 2 y equals , x squared  is shown below.

You can fold a parabola so that the two sides match exactly. This property is called symmetry. The fold or line that divides the parabola into two matching halves is called the axis of symmetry.

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