1. Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9
Factor each expression.
3. 3x2 – 12x
4. x2 – 9x + 18
5. x2 – 49

2. Objectives Vocabulary zero of a function root of an equation binomial
Solve quadratic equations by graphing or factoring.
Determine a quadratic function from its roots.
Vocabulary
zero of a function
root of an equation
binomial
trinomial

3. 8x is the sum of the O and I part of FOIL.
For “c” to be negative, “r” and “s” must have opposite signs

4. Factor the trinomial

5. Same general idea for factoring
but we need to look for the factors
of “ac” that combine to make “b”.

6. Special Cases
Difference of Squares – Product of a sum and
a difference.
Perfect Square Trinomials – The product of the
square of a sum or the square of a difference.

8. A zero of a function is a value of the input x that makes the output f(x) equal zero. The zeros of a function are the x-intercepts.
Unlike linear functions, which have no more than one zero, quadratic functions can have two zeros, as shown at right. These zeros are always symmetric about the axis of symmetry.

9. You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.
Functions have zeros or x-intercepts.
Equations have solutions or roots.
Reading Math

10. Example 1: Finding Zeros by Using a Graph or Table
Find the zeros of f(x) = x2 – 6x + 8 by using a graph and table.
Method 1 Graph the function f(x) = x2 – 6x + 8.

11. Example 1 Continued
Find the zeros of f(x) = x2 – 6x + 8 by using a graph and table.
Method 2 Use a calculator.
Enter y = x2 – 6x + 8 into a graphing calculator.
Both the table and the graph show that y = 0 at
x = 2 and x = 4. These are the zeros of the function.

12. Any object that is thrown or launched into the air, such as a baseball, basketball, or soccer ball, is a projectile. The general function that approximates the height h in feet of a projectile on Earth after
t seconds is given.
Note that this model has limitations because it does not account for air resistance, wind, and other real-world factors.

13. Example 3: Sports Application
A golf ball is hit from ground level with an initial vertical velocity of 80 ft/s. After how many seconds will the ball hit the ground?

14. Example 3 Continued
Check The graph of the function h(t) = –16t2 + 80t shows its zeros at 0 and 5.
–15
105 7 –3

15. Example 5: Using Zeros to Write Function Rules
If you know the zeros of a function, you can work backward to write a rule for the function
Example 5: Using Zeros to Write Function Rules
Write a quadratic function in standard form with zeros 4 and –7.

16. HW Day 1 wkst 1-30
Day 2 wkst 31-52
Day – 58 even, 27,47,