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}