Ch.4.8 Quadratic Functions Preview

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Presentation transcript:

Ch.4.8 Quadratic Functions Preview Warm Up California Standards Lesson Presentation

Warm Up 1. Evaluate x2 + 5x for x = 4 and x = –3. 36; –6 2. Generate ordered pairs for the function y = x2 + 2 for x-values –2, –1, 0, 1, and 2. x –2 –1 1 2 y 6 3

Ch.4.8 Quadratic Functions EQ: How can we identify, graph, and explain a quadratic function?

Solutions of the equation y = x2 are shown in the graph. Notice that the graph is not linear. The equation y = x2 is a quadratic equation. A quadratic equation in two variables can be written in the form y = ax2 + bx + c, where a, b, and c are real numbers and a ≠ 0.

Notice that the graph of y = x2 represents a function because each domain value is paired with exactly one range value. A function represented by a quadratic equation is a quadratic function.

The graph of a quadratic function is a curve called a parabola The graph of a quadratic function is a curve called a parabola. To graph a quadratic function, generate enough ordered pairs to see the shape of the parabola. Then connect the points with a smooth curve.

Additional Example 2B: Graphing Quadratic Functions Graph the quadratic function. y = –4x2 Make a table of values. Choose values of x and use them to find values of y. x –2 –1 1 2 y –4 –16 Graph the points. Then connect the points with a smooth curve.

When choosing values of x, be sure to choose positive values, negative values, and 0. Helpful Hint

Check It Out! Example 2a Graph each quadratic function. y = x2 + 2 Make a table of values. Choose values of x and use them to find values of y. x –2 –1 1 2 y 2 3 6 Graph the points. Then connect the points with a smooth curve.

Check It Out! Example 2b Graph the quadratic function. y = –3x2 + 1 Make a table of values. Choose values of x and use them to find values of y. x –2 –1 1 2 y 1 –2 –11 Graph the points. Then connect the points with a smooth curve.

1. Tear out Chapter 4. 8 Quadratic Functions, pages 335-338 and 2 1. Tear out Chapter 4.8 Quadratic Functions, pages 335-338 and 2. Chapter 4.9 Qualitative Graphs Pages 347-350.