Warmups

Factor2 10 25x x 2 29 49x y

2 5 6x x 29 24 16x x

11-3 Quadratic Formula

Objective: To solve a quadratic equation using the quadratic

formula.

Solve by factoring

2 8 5 0x x Wait a minute… HOLD UP... We can’t factor this!Are there roots?

Let’s check with the graph:Axis of symmetry?Vertex?Up or down?

Vocab

We solve a QUADRATIC EQUATION to find

ax2 + bx + c = 0

the ROOTS by graphing a

x-intercepts .

QUADRATIC FUNCTION

y = ax2 + bx + c

or using the QUADRATIC FORMULA

What is the Quadratic Formula?

x = 2a

at 2 am.

-b ± √ (b2 - 4ac )

A negative Boy couldn’t decidecouldn’t decidewhether or not to go to a radical party.The Boy was squareso he couldn’t get four Awesome Chicks.It was all over

YOU MUST MEMORIZE THIS!!!

Song time!!!

2 4

2

b b acx

a

Example 1

2x2 + 7x – 15 = 0

a =

b =

c =

3{ 5, }

2

2 4

2

b b acx

a

Example 2

3n2 – 8n – 2 = 0

a =

b =

c =

8 88 8 88{ , }

6 6

2 4

2

b b acx

a

{2.897, 0.230}

Example 3

y2 – 6y + 9 = 0

a =

b =

c =

{3 }dr

2 4

2

b b acx

a

Example 4

3x2 – x + 3 = 0

a =

b =

c = 2 4

2

b b acx

a

No real roots

TOO

1) 5x2 + 10x = 15

2) 3x2 – 10x = 0

Answers:

1) {-3,1}

2) {0,10/3}

Homework

Page 631 #14 - 22

Math Lab PRE warm up!!!

2 4

2

b b acx

a

Math Lab WarmupsSolve using quadratic formula

1) 5x2 + 10x = 15

2) 3x2 – 10x = 0

Answers:

1) {-3,1}

2) {0,10/3}