1. Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2

2. 2.2: Characteristics of Quadratic Functions
Objective: graph quadratic functions and identify their vertex and axis of symmetry

3. Axis of symmetry
The axis of symmetry is a line that divides a parabola into mirror images and passes through the vertex.
Cuts a parabola in half

4. Example 1: Plot the vertex at (- 3, 4).
Plot the vertex at (- 3, 4).
The axis of symmetry will be at the line vertically along the x value of the vertex.
x = -3
Plot two more points on the graph
(- 2, 2) and (- 1, - 4)
Draw the parabola through the points.

5. Practice
Graph y = 3(x - 2) Label the vertex and axis of symmetry.

6. Quadratic Functions

7. Quadratic Equation Standard Form: f(x) = ax2 + bx + c
Equation for the line of symmetry:
x-coordinate of vertex (find y-value by plugging in x-value and solving):

8. Steps to graphing a quadratic equation in standard form:
Standard form: f(x) = ax2 + bx + c
1.) Find x-coordinate of the vertex:
2.) Create table with x-coordinate of vertex in the middle and choose at least one value smaller than vertex and one value larger than vertex for x.
3.) Plug in values for x and solve for y.
4.) Plot points and draw parabola.

9. Graph f(x) = -4x2 + 8x+ 2

10. Quadratic Equation

11. Graphing using intercept form
f(x) = a(x – p)(x – q)
Plot the x-intercepts: points p and q
Find x-coordinate of vertex by averaging p and q:
Find y-coordinate of vertex by plugging in x-coordinate and solving. Plot the vertex.

12. Graph f(x) = (x + 2)(x – 2)

13. Graph y = 3(x + 3)(x + 5)

14. Finding Maximum and Minimum Values

15. Find the Maximum or Minimum Value

16. Find the Maximum or Minimum Value

17. Homework:
Textbook pg # 9, 29, 41, 56