Chapter 8.9 The Quadratic Formula.notebook
March 23, 2017
Bellwork:
Solve by Factoring (If you can't factor complete the square):
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1. x ­ 8x ­ 48 = 0
Homework Questions???
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2. 6x + 25x = 14
3. x2 ­ 18 = ­4x
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What methods have we used to solve an quadratic equation?
What method(s) only works sometimes?
8.9(a) The Quadratic Formula and the Discriminant
What method(s) always works?
Solve quadratic equations by using the quadratic formula
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Apr 18­8:32 AM
The Quadratic Formula Comes from Completing the Square
ax2 + bx + c = 0
Quadratic Formula:
Form
Factor out a:
(b/2)2:
If ax2 + bx + c = 0 and a ≠ 0, then
Add (b/2)2
times a on right:
Factor:
Solve:
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Chapter 8.9 The Quadratic Formula.notebook
Before we can use the quadratic formula we need to get the equation in standard form ax2 + bx + c = 0.
March 23, 2017
Example 1: Solve 7x ­ 2 ­ 4x = ­2x2 by using the quadratic formula.
1) 6x2 = ­9
Step 1: Put into standard form
2) 2x2 + 8 ­ 9x = 0
Step 2: Identify a, b, c values
3) 7x ­ 10 = 3x2
Step 3: Substitute values of a, b, c into quadratic equation.
Step 4: Solve (order of operations)
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You Try 1: Solve x2 ­ 2x = 8 by using the quadratic formula.
Example 2: Solve 2x2 + 4x ­ 5x2 = ­3 by using the quadratic formula.
Step 1: Put into standard form
Step 1: Step 2: Identify a, b, c values
Step 2: Step 3: Substitute values of a, b, c into quadratic equation.
Step 3: Step 4:
Step 4: Solve (order of operations)
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You Try 2: Solve x2 + 4x ­ 4 = 3 ­ x2 by using the quadratic formula.
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You Try 3: Solve ­ 8x + 16 + 9x2 = 16x by using the quadratic formula.
Step 1: Step 1: Step 2: Step 2: Step 3: Step 3: Step 4:
Step 4:
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Chapter 8.9 The Quadratic Formula.notebook
March 23, 2017
We are going to talk about a portion of the quadratic formula called the discriminant.
The Discriminant of Quadratic Equation ax2 + bx + c = 0
The discriminant of a quadratic formula is b2 ­ 4ac.
Discriminant Number of Solutions
b2 ­ 4ac > 0
two solutions
b2 ­ 4ac = 0
one solution
b2 ­ 4ac < 0
no solution
It is used to help tell how many solutions a quadratic equation will have. Apr 21­4:18 PM
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Homework
P. 587­588 #1­37, 49­51 (odds)
skip #23
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