1. Warm-up
1. Solve the following quadratic equation by Completing the Square:
2x2 - 20x + 16 = 0
2. Convert the following quadratic equation to vertex format
y = 3x2 – 12x + 23

2. Section 4-8 The Quadratic Formula
Chapter 4
Section 4-8
The Quadratic Formula

3. Objectives
I can use the Quadratic Formula to solve for the solutions of any quadratic equation

4. Quadratic Review Quadratic Equation in standard format:
y = ax2 + bx + c
Solutions (roots) are where the graph crosses or touches the x-axis.
Solutions can be real or imaginary

5. Types of Solutions 2 Real Solutions 1 Real Solution
2 Imaginary Solutions

6. Key Concept for this Section
What happens when you square any number like below:
x2 = ?
It is always POSITIVE!!
This is always the biggest mistake in this section

7. Key Concept #2
What happens when you subtract a negative number like below:
= ?
It becomes ADDITION!!
This is 2nd biggest error on this unit!

8. The Quadratic Formula
The solutions of any quadratic equation in the format ax2 + bx + c = 0, where a  0, are given by the following formula:
x =
The quadratic equation must be set equal to ZERO before using this formula!!

9. Example 1 x2 – 7x = 18 First set equation equal to 0
x2 – 7x – 18 = 0 Now identify a, b, and c
a = 1, b = -7, c = Now plug into formula
x = =
x = =
x = = 18/2 0r -4/2
x = 9 or -2

10. Your Turn
Solve the following in your notes:
-3x2 + 4x – 4 = 0
Roots:

11. Another Attempt Solve the following in your notes: x2 + 9x – 11 = 0
Roots:

12. Solve an equation with two real solutions
EXAMPLE 1
Solve an equation with two real solutions
Solve x2 + 3x = 2.
x2 + 3x = 2
Write original equation.
x2 + 3x – 2 = 0
Write in standard form.
x =
– b + b2 – 4ac 2a
Quadratic formula
x =
– – 4(1)(–2)
2(1)
a = 1, b = 3, c = –2
x =
– 3 + 17 2
Simplify.
The solutions are
x =
– 3 + 17 2
0.56 and
– 3 –
– 3.56.
ANSWER

13. Solve an equation with imaginary solutions
EXAMPLE 3
Solve an equation with imaginary solutions
Solve –x2 + 4x = 5.
–x2 + 4x = 5
Write original equation.
–x2 + 4x – 5 = 0.
Write in standard form.
x =
– 42– 4(– 1)(– 5)
2(– 1)
a = –1, b = 4, c = –5
x =
– – 4
– 2
Simplify.
– 4+ 2i
x =
– 2
Rewrite using the imaginary unit i.
x = 2 + i
Simplify.
The solution is 2 + i and 2 – i.
ANSWER

14. Homework
WS 6-4
Factoring Quiz