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

2. 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

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

4. 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.

5. 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.

6. 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.

7. 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.

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

9. 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.

10. 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.

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