Download 2017-4-3 quadratic formula.notebook

2017­4­3 quadratic formula.notebook
April 03, 2017
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Section 9.5
pg. 521 #3-29 odd
Chapter 9 test Thursday
extra help Thurs. at 7:20
HW Answers
2017­4­3 quadratic formula.notebook
Today's Objective:
Using the Quadratic Formula
April 03, 2017
2017­4­3 quadratic formula.notebook
April 03, 2017
What ways do we solve a quadratic if we cannot factor it?
Let's use some algebra wizardry to solve for x.
a2 + bx + c = 0
Use the quadratic equation
The real solutions of the quadratic equation
2
ax +bx+c = 0 can be found using
-b ± √b2 - 4ac
x =
2a
2
if a = 0 and b - 4ac > 0
2017­4­3 quadratic formula.notebook
April 03, 2017
Solve the following using the quadratic
formula:
x2 - 2x -12 = 0
-b ± √b2 - 4ac
2a
a=
b=
c=
Solve 2x2 − 5x + 3 = 0 using the Quadratic Formula.
-b ± √b2 - 4ac
2a
2017­4­3 quadratic formula.notebook
April 03, 2017
Solve the following using the quadratic formula
x2 - 2x + 1 = 0
a=
b=
c=
-b ± √b2 - 4ac
2a
How many solutions are there?
Solve the following using the quadratic formula
3b2 + 4b + 8 = 0
-b ± √b2 - 4ac
2a
a=
b=
c=
How many solutions are there?
2017­4­3 quadratic formula.notebook
April 03, 2017
The discriminant
It tells you....
-the number of real roots Formula:
-the number of x-intercepts
b2 - 4ac
REMEMBER: Roots = Solution = Zeroes = X­Intercepts
When....
Discriminant is positive the quadratic has 2 real solutions
2017­4­3 quadratic formula.notebook
April 03, 2017
When....
Discriminant is zero the quadratic has 1 real solution
When....
Discriminant is negative the quadratic has no real solutions
2017­4­3 quadratic formula.notebook
Determine the number of real solutions of the equation.
7. −x2 + 4x − 4 = 0
8. 6x2 + 2x = −1
9. x2 = 7x − 1
April 03, 2017
2017­4­3 quadratic formula.notebook
April 03, 2017
Solve the equation using any method. x2 + 11x − 12 = 0
9x2 − 5 = 4
2
5x2 − x − 1 = 0
x = 2x − 5