1. Section 2.1
Quadratic Functions

2. Objective By following instructions students will be able to:
Analyze graphs of quadratic functions.
Write quadratic functions in standard form and use the results to sketch graphs of functions.
Use quadratic functions to model and solve real-life problems.

3. Polynomial Functions Constant functions - numbers
Linear functions – lines
Quadratic functions - parabolas

4. Parabolas in Real Life

8. Example 1: Describe how the graph of each function is related to the graph of .
a) b)
c) d)

9. Standard (Vertex) Form of a Quadratic Function
If a>0, parabola opens up
If a<0, parabola opens down
The vertex of the parabola is (h,k)

10. Example 2:
Write the quadratic function in vertex form. Identify the vertex.

11. Example 3:
Write the quadratic function in vertex form. Identify the vertex and any x-intercepts.

12. U-TRY #1
Sketch the graph of the quadratic function. Identify the vertex and x-intercepts. a) b) c)

13. Example 4:
Find the standard form of the equation for the parabola that has its vertex at (1,2) and passes through the point (3,-6).

14. Maximum/Minimum Point
The maximum or minimum point is the vertex of the parabola.

16. Example 5:
An angry bird is thrown 3 feet above the ground at a velocity of 100ft per second and at an angle of 45 degrees with respect to level ground. The path of the angry bird is given by the function where f(x) is how far the bird is away from the ground and x is the horizontal distance from where the bird is thrown. What is the maximum height reached by the angry bird?

17. U-TRY #2
a) Find the quadratic function that has a vertex of (4,-1) and whose graph passes through the point (2,3).
b) The height y (in feet) of a ball thrown by a child is
where x is the horizontal distance (in feet) from where the ball is thrown.
Sketch the graph of the ball.
How high is the ball when it leaves the child’s hand? (Hint: find y, when x=0).
How far from the child does the ball strike the ground?

18. Example 6:
According to a survey conducted by Independent Sector, the percent of their income that Americans give to charities is related to their household income. For families with an annual income of $100,000 or less, the percent is approximately Where P is the percent of annual income given and x is the annual income (in thousands of dollars). According to this model, what income level corresponds to the minimum percent of charitable contributions?

19. Revisit Objective Did we… Analyze graphs of quadratic functions?
Write quadratic functions in standard form and use the results to sketch graphs of functions?
Use quadratic functions to model and solve real-life problems?

20. Homework
HW: I: pg 131 #s 1, 7, 22
II: pg 143 #s 1-8, 11, 12, ODD, 47, 57, 71
III: pg 146 #s 79, 80