1. Factor completely 6𝑥 2 +28𝑥−10
I can graph quadratics.
Warm Up
Factor completely 6𝑥 2 +28𝑥−10
2. Find the x- and y- intercepts
𝑥 2 +3𝑥−40=0

2. Factor completely 6𝑥 2 +28𝑥−10 𝟐(𝟑𝒙−𝟏)(𝒙+𝟓)
Warm Up
Factor completely 6𝑥 2 +28𝑥−10
𝟐(𝟑𝒙−𝟏)(𝒙+𝟓)
Have student volunteers talk through how to factor. Discuss the idea of “factoring completely” by taking the greatest common factor out first.

3. 2. Find the x- and y- intercepts 𝑥 2 +3𝑥−40=0
Warm Up
2. Find the x- and y- intercepts
𝑥 2 +3𝑥−40=0
We haven’t talked about using zero product property to find x-intercetps, that’s what will be covered in today’s lesson. Review finding the y-intercept and tell them the answer to the x-intercepts.
x-int: (-8,0) and (5, 0) y-int: (0, -40)

4. Investigate a Parabola
Page 340, #8-43
Each group investigates an equation and makes a complete graph with the knowledge they already have. All equations have a=1 or -1. Assign each pair a different parabola from the list on page 341.
Investigate a Parabola

5. Describe your parabola!
Symmetry
High/Low point
Any special points
The shape
Problem 8-43 & 8-44 in book. You can use handout for classwork part A, or just use the textbook and have students put answers in comp book. Assign each group a different parabola from problem 8-43, listed above.

6. Vertex
Line of Symmetry

7. Downward Parabolas
y-axis
Vertex
x-axis
The Solutions
(x-intercepts)

8. Quadratics Vocabulary
Vertex: The highest or lowest point on a parabola X-Intercept(s): Where the graph crosses the x-axis. The “solutions” to a quadratic equation.

9. Quadratics Vocabulary
Y-Intercept: Where the graph crosses the y-axis Line of Symmetry: The line that divides the parabola into mirror images. If you fold your graph on the line of symmetry, the two sides will match perfectly.

10. Your vertex? Your y-intercept? Your x-intercept(s)?
Line of Symmetry
Your vertex?
Your y-intercept?
Your x-intercept(s)?
Recap of classwork Part A
Your line of symmetry?

11. BREAK!

12. I’m Thinking of a Parabola
The y-intercept of my parabola is at
(0, –8), can you sketch its graph?

13. I’m Thinking of a Parabola
The x-intercepts of my parabola are (-2,0) and (4,0) and the
y-intercept of my parabola is at (0, –8) , can you sketch its graph?

14. I’m Thinking of a Parabola
The vertex of my parabola is (1,-9), the
x-intercepts of my parabola are (-2,0) and (4,0) and the
y-intercept of my parabola is at (0, –8). Can you sketch its graph?

15. What information do you need to graph a parabola?
Line of Symmetry

16. 1. 5∙𝑥=0 2. 1.65∙ 𝑥+5 =0 3. 𝑥∙𝑦=0 What do you notice??
Solve each equation
1. 5∙𝑥= ∙ 𝑥+5 =0 3. 𝑥∙𝑦=0
What do you notice??

17. Zero product property notes
𝑥+3 ∙ 𝑥 −5 =0
𝑥+3 =0
𝑥 −5=0
−3 −3
+5 +5
𝑥=−3
𝑥=5

18. Set each factor equal to 0
Zero Product Property
2 𝑥 2 +5𝑥−12= 0
Factor
2𝑥−3 𝑥+4 =0
Set each factor equal to 0
2𝑥−3=0 𝒐𝒓 𝑥+4=0
Solve
𝑥= 𝒐𝒓 𝑥=−4

19. Zero Product Property Solve 1. (𝑥−4)(𝑥−5)=0 2. (2𝑥+2)(3𝑥−1)=0
Now try a few of these on your own.
Solve
1. (𝑥−4)(𝑥−5)=0
2. (2𝑥+2)(3𝑥−1)=0
3. 2𝑥(𝑥+2)=0
4. 𝑥 2 +8𝑥−33=0

20. Homework:
Page 349 & 350 #8-65 to 8-69