1. Quiz review
Direction of Opening
Y – intercept
Vertex
AOS
Min/Max Value
Number of solutions
Solutions
Domain and Range
Increasing Decreasing

2. Quiz Review

3. On the Calculator On the Calculator: Min/Max (Vertex) AOS Zeros
**Put equation in y1
**Hit 2nd Trace
**Follow directions on Calculator

4. Properties of quadratic equations - equation
September 26th

5. Standard form of quadratic equations
y = ax2 + bx + c a ≠ 0

6. What does the equation of a quadratic function tell us?
Let’s look at y = x2 and y = -x2:
Think-Pair-Share:
What do you notice about these two graphs? What is the difference between the two equations? What do you think the difference means?
Parabola

7. What does the equation of a quadratic function tell us?
Direction of opening:
If a>0, the direction of opening is UP.
If a<0, the direction of opening is DOWN.
Example: y = 5x2 + 10x – 7

8. What does the equation of a quadratic function tell us?
Graph the equation in you calculator: y = x2 + 4x – 5 What is the y – intercept?

9. What does the equation of a quadratic function tell us?
y – intercept: In standard form, c gives us the y-intercept: y = ax2 + bx + c Example: y = 5x2 + 10x – 7

10. What is the direction of opening and y – intercept of the equations?
1. y = -8x2 + 2x + 1
2. y = 6x2 – 24x - 4

11. What does the equation of a quadratic function tell us?
Axis of Symmetry (AOS): we can use the formula to find the AOS.
Example: y = -x2 + 8x + 16

12. What does the equation of a quadratic function tell us?
Vertex: plug the AOS in for x and find the y value of the vertex. Example: y = -x2 + 8x + 16

13. Find the AOS and vertex
y = -8x2 + 2x y = 6x2 – 24x - 4

14. What does the equation of a quadratic function tell us?
Maximum/Minimum: highest/lowest point
If a < 0, the graph has a ______________
If a > 0, the graph has a ______________
The maximum/minimum value is the y – value of the vertex.
Example: y = -x2 + 8x + 16

15. Properties – Practice using the equation
1. y = x2 + 6x + 8 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value:

16. Warm up -x2 + 10x + 25 2x2 – 4x – 6 Direction of Opening?
For the two quadratics answer these questions:
Direction of Opening?
Y – intercept?
AOS?
Vertex?

17. Properties – Review using the equation
y = -2x2 + 12x + 16 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value: Sketch the Graph:

18. Properties – Review using the equation
y = 2x2 + 24x + 20 Direction of Opening: y – intercept: AOS: Vertex: Max or Min Value: Sketch the Graph:

19. Activity
You and your partner will either have a picture of a graph or the equation of the graph. You should take a couple minutes to right down everything you know about your graph/equation. Then when I say, walk around the room and find the pair with the matching graph/equation. Example: Matching Graph to Equation

20. Flex - Factoring Review
Factor the following expressions:
x2 – 15x + 50: (x – 5)(x – 10)
12xy – 4y + 9x – 3: (4y + 3)(3x – 1)
x2y - 3x2 – 8y - 24: (x2 – 8)(y – 3)
x2 – 36: (x – 6)(x + 6)
20x2 – 16x: 4x(5x – 4)
4x2 - 24x + 36: 4(x – 3)(x – 3)
2x3 + 12x2 + 16x: 2x(x + 4)(x + 2)
x2 - 5x - 14: (x – 7)(x + 2)
15ab – 5b + 9a – 3: (5b – 3)(3a – 1)

21. Zeros, roots, x – intercepts, solutions
Remember: factor the equation then set each set of parentheses equal to 0 and solve for x.
Example (solve by factoring): y = 3x2 + 2x – 5

22. You try (x + 5)(x – 1) = 0 (2y – 1)(3y + 2) = 0 (3x – 3)(4x – 8) = 0
(7n – 14)(6n – 3) = 0

23. Solve by factoring
1. y = x2 - 10x -  y = -3x2 + 12

24. Solve by factoring
3. y = -2x2 + 6x  y = 4x2 - 8x - 32

25. Solve by factoring
5. y = 3x2 – 9x y = 3x2 + 4x – 4

26. Stations Review
Complete All Stations – Due at the end of class time!

27. Homework
Worksheet