Warm-Up: September 30 / October 1, 2015
Factor each expression
1.
2x2 + 7x – 4
2.
4x2 – 13x + 3
3.
9x2 + 9x + 2
Homework Questions?
Quadratic Equations
Section P.8
Essential Question

How can we solve quadratic equations?
Quadratic Equations


A quadratic is a second-degree polynomial
The general form is
2
ax  bx  c  0
a, b, c  R , a  0
Zero Product Property
If AB = 0, then A = 0 or B = 0
 Use to solve a quadratic
1. Write the quadratic in general form
2. Factor the quadratic
3. Set each factor equal to zero
4. Solve each equation

You-Try #1: Solve by Factoring
a) 3x  9 x  0
2
b) 2 x  x  1
2
Solving Quadratics Using Square Roots
Use when you have x2 + c = 0 (b=0)
 Also used when you have an expression squared
and a number (u2=d)
1. Get the squared term by itself
2. Take the square root of both sides
3. Remember ±

You-Try #2: Solve with Square Root
a) 4 x  24
2
b)
 x  5
2
 13
Completing the Square

Given 𝑥 2 + 𝑏𝑥, we can create a perfect square
trinomial by dividing b by 2, squaring it, and adding it
2
b
b 
x  bx      x  
2
2 
2
2


When solving, you must have one side be “𝑥 2 + 𝑏𝑥”
Remember that whatever you add to one side, you
must add to the other side
Example 3: Completing the Square (#27-37)

Determine the constant that should be added to the
binomial so that it becomes a perfect square
trinomial. Then write and factor the trinomial
x  14 x
2
You-Try #3: Completing the Square (#27-37)

Determine the constant that should be added to the
binomial so that it becomes a perfect square
trinomial. Then write and factor the trinomial
4
x  x
5
2
Example 4a: Solving by Completing the Square
2 x  5x  3  0
2
You-Try #4: Solving by Completing the Square
2x  4x 1  0
2
Example 4b: Solving by Completing the Square
2
ax  bx  c  0
The Quadratic Formula
 b  b  4ac
x
2a
2
You-Try #5: Solving using Quadratic Formula
3x  6 x  1
2
The Discriminant: b2 – 4ac

The value of the discriminant tells you the number
and type of solutions you will have
Discriminant
b2 – 4ac < 0
b2 – 4ac = 0
b2 – 4ac > 0
Is a perfect square
b2 – 4ac > 0
Not a perfect square
Solutions to ax2 + bx + c = 0
The Discriminant: b2 – 4ac

The value of the discriminant tells you the number
and type of solutions you will have
Discriminant
Solutions to ax2 + bx + c = 0
b2 – 4ac < 0
No real solutions
b2 – 4ac = 0
One real solution
b2 – 4ac > 0
Is a perfect square
Two rational solutions
b2 – 4ac > 0
Not a perfect square
Two irrational solutions
b
x
2a
Example 6: Using the Discriminant (#63-69)

Compute the discriminant. What does the
discriminant indicate about the number and type of
solutions?
3x  2 x  1
2
You-Try #6: Using the Discriminant (#63-69)

Compute the discriminant. What does the
discriminant indicate about the number and type of
solutions?
2 x  11x  6  0
2
What method should I use?
1.
2.
3.
4.

If 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 can easily be factored, then factor
and use zero product property.
If 𝑏 = 0, use square root method
If you have something in parentheses squared, use
square root method.
If 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 cannot be factored, use quadratic
formula
See page 94 if you need more help choosing what
method to use.
Assignment


Read Section P.8
Page 97 #1-93 Every Other Odd, 99, 119