1. 5-26. WHAT DO YOU NEED TO SKETCH A PARABOLA?
How many points do you need in order to sketch a parabola? One? Ten?  Fifty?  Think about this as you answer the questions below.
Can you make a sketch of a parabola if you only know where its y-intercept is?  For example, if the y-intercept of a parabola is (0, –15), can you sketch its graph?  Why or why not?
No; the y-intercept is not enough information because the width and which way the parabola opens is not specified.
What about two x-intercepts of a parabola?  If you only know the x-intercepts, can you sketch the parabola?  For example, if the x-intercepts are (–3, 0) and (5, 0), can you sketch the parabola?
No; the parabola could vary in “steepness”, vertex, and/or which way it opens.
Can you make a sketch of a parabola with only two x-intercepts and the y-intercept?  To test this idea, sketch the graph of a parabola that has x-intercepts (–3, 0) and (5, 0) and y-intercept (0, –15).
Yes (but you do not know exactly where the vertex is)
Warm Up

2. HW: 5-32 through 5-37
5.1.3 Zero Product Property
January 19, 2016

3. LO: SWBAT explain the zero product property.
Objectives
CO: SWBAT sketch the graph of a quadratic function, using its intercepts.
LO: SWBAT explain the zero product property.

4. 5-27.  In the previous problem, you learned that if you know the intercepts of a parabola, then you can sketch its graph without making a table.  But, how can you determine the intercepts of a parabola from its equation?
What is true about the value of y for all x-intercepts?  What is true about the value of x for all y-intercepts?
y = 0 for all x-intercepts and x = 0 for all y-intercepts.
What is the y-intercept of the graph of y = 2x2 + 5x – 12?
y = 2(0)2 + 5(0) – 12
(0, –12)
What equation would you need to solve to determine the x‑intercepts of the graph of y = 2x2 + 5x – 12?
0 = 2x2 + 5x – 12
The solutions to the equation 2x2 + 5x – 12 = 0 are called the zeros of the function y = 2x2 + 5x − 12.  At this point, can you algebraically solve the equation 2x2 + 5x − 12 = 0?  Explain why or why not.
Not yet, because it has an x2 term.
TEam

5. 5-28. ZERO PRODUCT PROPERTY
The equation you wrote in part (c) of problem 5-27 is called a quadratic equation.  To solve it, you need to examine what you know about zero.  Study the special properties of zero below. 
Nathan, Nancy, and Gaston are playing a game where Nathan and Nancy each think of a number and then give Gaston a clue about their numbers.  Using the clue, Gaston must tell them everything that he knows about their numbers.
Nathan and Nancy’s first clue for Gaston is that when you multiply their numbers together, the result is zero.  What conclusion can Gaston make?
At least one of the two numbers must be zero.
Disappointed that Gaston came close to figuring out their numbers, Nathan and Nancy invite Nadia over to make things harder.  Nathan, Nancy, and Nadia all think of secret numbers.  This time Gaston is told that when their three secret numbers are multiplied together, the answer is zero.  What can Gaston conclude this time?
At least one of the three numbers must be zero.
Does it matter how many numbers are multiplied?  If the product is zero, what do you know about at least one of the numbers?  This property is called the Zero Product Property. 
Learning Log - Zero Product Property
If the product of two or more numbers is zero, then one of the numbers must be zero.
Then ask two students to come to the front of the class.  Give each student a secret number that is not zero or prime.  Ask the volunteers to share their numbers with each other and to tell the class what the product of their numbers is.  Then ask the class as a whole what they can conclude about the secret numbers; the first time through they will not be able to guess either of the numbers easily.  Then, repeat the activity, making sure that one of the two numbers is zero, announce the product of zero, and ask students to guess again.  Repeat again with three students to ensure that students understand that the Zero Product Propertyapplies even when there are more than two numbers multiplied.

6. Rewrite the equation as a product equal to zero.
5-29.  Now you will apply the Zero Product Property to solve the quadratic equation 2x2 + 5x – 12 = 0 from problem 5-27.
Rewrite the equation as a product equal to zero.
0 = (2x – 3)(x + 4)
Now that the equation is written as a product of factors equal to zero, you can use the Zero Product Property to solve it.  Use one factor at a time and determine what x-value makes it equal to zero.
2x – 3 = 0 or x + 4 = 0
2x = 3 x = -4
x = 3 2
The x-intercepts are at ( 3 2 , 0) and (–4, 0).
With one more piece of information, you can sketch the graph of the parabola y = 2x2 + 5x – 12.  What is this missing piece of information?  Sketch the graph.
The y‑intercept is (0, –12).

7. 5-30. Another useful point on a parabola is the vertex
5-30.  Another useful point on a parabola is the vertex.  How can you use the x-intercepts of a parabola to help you locate the vertex?
​Use the Zero Product Property to determine the x-intercepts of the parabola y = x2 + 4x – 5.
0 = (x + 5)(x – 1)
x + 5 = 0 or x – 1 = 0
x = x = 1
(-5,0) and (1,0)
Work with your team to use the x-intercepts to determine the vertex of the parabola.
−5+1 2 =−2
y = (-2)2 + 4(-2) – 5
(-2,-9)
Sketch the parabola y = x2 + 4x – 5.
TEam