Solving Quadratic Equations
WARM UP May 22, 2015
Solve quadratic equations by Completing the square.
x2 + 6x + 8 = 0
5k2= 60 − 20k
n2 − 2n − 3 = 0
Solving Quadratic Equations
The Quadratic Formula
The quadratic formula is used to solve any quadratic equation.
Standard form of a quadratic equation is:
ax 2  bx  c  0
The quadratic formula is:
b  b2  4ac
x
2a
Solving Quadratic Equations
ax 2  bx  c  0
x2  4x  8  0
a 1
b4
2x2  x  0
c 8
3x 2  5 x  6  0
a 3
b  b  4ac
x
2a
2
b  5 c  6
a 2
b 1
c 0
x 2  10
x 2  10  0
a  1 b  0 c  10
Solving Quadratic Equations
The Quadratic Formula
ax 2  bx  c  0
x 2  3x  2  0
a  1 b  3 c  2
x
  3 
 3  4 1 2 
2 1
3 9 8
x
2
2
3 1
x
2
3 1
x
2
b  b2  4ac
x
2a
3 1
x
2
3 1
3 1
x
x
2
2
2
4
x
x
2
2
x2
x 1
8.2 – Solving Quadratic Equations
The Quadratic Formula
b  b  4ac
x
2a
2
ax  bx  c  0
2
2 x2  x  5  0
a 2
x
b  1 c  5
  1 
1  1  40
x
4
 1  4  2  5
2  2
2
1  41
x
4
Quadratic Formula Musical ♪♫
Solving Quadratic Equations
b  b  4ac
x
2a
The Quadratic Formula
Do Now!
m2 − 5m − 14 = 0
2
2x2 + 3x − 20 = 0
Solving Quadratic Equations
Unit 4 Test Preparation
DOK 1]
3 problems of Factoring – what you need to know:
GCF, Difference of squares
Trinomial Factoring with/without
leading coefficient
DOK 2] 2 problems of solving quadratic equation
what you need to know: Completing the square method
Quadratic formula
DOK 3] Let’s start with a goal problem
Solving Quadratic Equations
Okay! Now we can solve quadratic equations
by using Quadratic Formula or completing the square.
Wait! But then…..Can we try another method to solve the
equation as well? Just like ______________.
x 2  3x  2  0
 x 1  x  2
x 1  0
x 1
0
x2  0
x2
Solving Quadratic Equations
Goal Problem DOK 3]
What is a possible quadratic equation for the following solutions?
x=1 or x=2
Practice your own!
What is a possible quadratic equation for the following solutions?
x=3 or x=-4
Practice your own!
What is a possible quadratic equation for the following solutions?
x=3 or x=-4