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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!!
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?
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
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
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