1. Today:
 Welcome Back
 Notebook, pencil, calculator ready
 Review for final exam and test

2. Reminders:
 All Khan Academy Due by 3:00 & 9:00
 There will be a test on Friday. We will review
today and tomorrow.
 The unit on Quadratics is almost finished; we
begin our unit on radicals tomorrow.
 Next Khan will be given Monday.
 Classwork: Show all work, and most
importantly, complete & turn in.
 We are reviewing for the final exam first, then
our test Friday, including new material. Get your
pencil, calculator, and WORK THE PROBLEMS!!

3. Warm-Up/Final Exam Review:

4. Warm-Up/Final Exam Review:

5. Warm-Up/Final Exam Review:?
Simplify:

6. Warm-Up/Final Exam Review:
Drawing a number line helps, especially with the negative numbers
Which relation below is not a function?
A. B.

7. Quadratic Review/Test Prep:

8. no
1. Without graphing, tell whether (3, 12) is on the graph of
y = 2x2 – 5.
Quadratic Review/Test Prep:
2. What is the vertex of the equation:
3.
What method are
you using to solve?

9. Write a Quadratic Equation Given Roots

10. Write a Quadratic Equation Given Roots
If all you had were the roots of a quadratic equation.
Could you write the equation that produced the roots?
The roots of a quadratic equation are -2 and 6. Write a
quadratic model with leading coefficient of 1.
Work backwards: start with your answer
x = -2 or x = 6 solutions/roots
x + 2 = 0 or x – 6 = 0 equation for roots
(x + 2)(x - 6) = 0 quadratic equation
x² - 6x + 2x – 12 = 0 distribute using FOIL
x² - 4x – 12 = 0 combine like terms
This is the quadratic equation with roots
{-2, 6}

11. The roots of a quadratic equation are 7 and - 1. Write a
quadratic equation with leading coefficient of 1.
x - 7 = 0 or x + 1 = 0 equation for roots
x = 7 or x = - 1 solutions/roots
x² - 6x – 7 = 0 combine like terms
Write a Quadratic Equation Given Roots

12. A parabola crosses the y axis at -3 and 1.
a. Write a quadratic function where x is a function of
y: f(y) =b. find the AOS, vertex, then graph
Write a Quadratic Equation Given Roots
y2
+ 2y - 3
Vertex is: -4,-1
Axis of Symmetry is: -4,-1
•
•
•
•
•
Plot for y = 2, then graph

13. Completing the Square
6x2
+ 24x – 84 = 0

14. Take the square root of
both sides
2. When graphing, change
the equation to:
y = (x – 2)2
- 16
4x3
= 9x

15. Rationalizing the Denominator

16. We will start with a simple case of a radical in the
denominator. This must be removed. Why?
Rationalizing the Denominator
By "rationalizing the denominator." (Changing the
denominator from a radical number to a rational one.)
This is done by removing the square root from the
denominator. How can we make the denominator 2?
It’s just a generally agreed upon thing in math, that’s
all. How is it done?
Simplify: Finally:

17. Always factor out
perfect squares
Rationalizing the Denominator

18. The Quadratic Formula
Solve using the Quadratic Formula
3x2 = 5x - 2
x =
5 + 1
6 = 1, 2/3