1. LEARNING GOALS - LESSON 5.3 – DAY 1
Warm Up
Find the x-intercept of the function.
f(x) = –3x + 9
LEARNING GOALS - LESSON 5.3 – DAY 1
5.3.1: Use a graph and table to find zeros of a quadratic function.
5.3.2: Find zeros by factoring, ac method, square roots, GCF
A _____ of a function is a value of the input x that makes the output f(x) equal zero. (“When you plug in ______ for _____.”) The zeros of a function are the x-intercepts.
What does a zero look like in an equation?
What does a zero look like on a graph?
How many zeros can a parabola have?

2. 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 The graph opens __________.
2. The axis of symmetry is:__
The vertex is:(_____,_____)
The y-intercept is: ______
Method 2 Use a calculator: Enter y = x2 – 6x + 8 into a graphing calculator.
Step 1: Put equation in Y= menu.
Step 2: Push Zoom and select option 0: Zoom Fit
Step 3: Look for possible x values that will have a zero.
Step 4: Push 2nd and then TABLE
Step 5: Look for x values that give you a 0 in the y column OR
Step 6: Push GRAPH
Step 7: Push 2nd and then TRACE
Step 8: Select option 2: Zero
Step 9: Move cursor to the left of a suspected zero; hit enter.
Step 10: Move cursor to the right of the suspected zero; hit enter.
Step 11: Hit enter one more time for good measure.

3. B. Find the zeros of g(x) = –x2 – 2x + 3 by using a graph
and a table with your calculator.
YOU CAN ALSO FIND ZEROS BY USING ALGEBRA.
For example, to find the zeros of f(x)= x2 + 2x – 3, you can set the function equal to zero.
We do this because:
SETTING THE FUNCTION = to _____ WILL GIVE US THE ZEROS or _____- VALUES OF THE FUNCTION ARE WHERE IT CROSSES THE ____-_________ or WHERE THE FUCNTIONS VALUE IS _________.
The solution to a quadratic equation of the form ax2 + bx + c = 0 are roots. The _________ of an equation are the values of the variable that make the equation true.
Functions have zeros or x-intercepts.
Equations have solutions or roots.
Reading Math

4. Example 2: Finding Zeros by Factoring
You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.
ZERO PRODUCT PROPERTY:
Example 2: Finding Zeros by Factoring
A. Find the zeros of the function by factoring.
f(x) = x2 – 4x – 12
Set the function equal to 0.
Factor using _________________:
Find factors of ______ that add to ____.
Apply the Zero Product Property.
Solve each equation.
B. Find the zeros of the function by factoring.
g(x) = 3x2 + 18x
C. Find the zeros of the function by factoring.
f(x)= x2 – 5x – 6
D. Find the zeros of the function by factoring.

5. LEARNING GOALS - LESSON 5.3 - DAY 2
5.3.3: Find roots of a quadratic using special factors.
5.3.4: Write a quadratic function with given zeros.
5.3.5: Find Max/Min height of a ball.
Example 3: Find Roots by Using Special Factors
A. Find the roots of the equation by factoring.
4x2 = 25
B. Find the roots of the equation by factoring.
18x2 = 48x – 32
C. Find the roots of the equation by factoring.
Rewrite in standard form.
x2 – 4x = –4
Factor the perfect-square trinomial.
Apply the Zero Product Property.
Solve each equation.
Solve each equation.
D. Find the roots of the equation by factoring.
25x2 = 9

6. Example 4: 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 4: Using Zeros to Write Function Rules
Write a quadratic function in standard form with zeros 4 and –7.
Write the zeros as solutions for two equations.
Rewrite each equation so that it equals 0.
Apply the converse of the Zero Product Property to write a product that equals 0.
Multiply the binomials.
Replace 0 with f(x).
Write a quadratic function in standard form with zeros 5 and –5.
NOTE: there are many quadratic functions with the same zeros.
For example, the functions: A. f(x) = x2 – x – B. g(x) = –x2 + x C. h(x) = 2x2 – 2x – 4
So writing function rules using zeros does not give a specific function
A B C
all have zeros at 2 and –1

7. Example 6: Sports Application
Any object that is thrown or launched into the air is a __________ . The general function that approximates the height h in feet of a projectile on Earth after t seconds is given. (The formula below does not account for ________________ or _________________.
h(t) = –16t2 + v0t + h0
Example 6: 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?
h(t) = –16t2 + v0t + h0
Write the general projectile function.
Substitute ______ for v0 and ______ for h0.
The ball will hit the ground when its height is ________.
Set h(t) equal to ______.
Factor: The GCF is ______t.
Apply the Zero Product Property.
Solve each equation.
B. A football is kicked from ground level with an initial
vertical velocity of 48 ft/s. How long is the ball in the air?
h(t) = –16t2 + v0t + h0
The ball will hit the ground when its height is __________