1. 5.5 Quadratic Equations
(Day 1)

2. Standard form of a quadratic equation
ax2 + bx + c = 0, where a ≠ 0
Zero-Product Property
For every real number a and b, if ,
ab = 0
then or
a = 0
b = 0
EX 1
(x + 5)(5x – 6) = 0
x + 5 = 0 or
5x – 6 = 0
Short cut:
x = or
- 5
5x = 6
{ , }
- 5
x = 5

3. ( )( ) + – ( )( ) + + { , } { , } ( )( ) ( )( ) – – + – { , } { , }
Solving by Factoring
White Boards
Together L
1. s2 – 3s – 10 = h2 + 10h = – 21 1, 10 L
( )( ) s + – 2 s 5
= 0 2, 5
h2 + 10h = 0
+ 21 1, 21
( )( ) + + 3, 7 h 3 h 7
= 0
+ 2s =
OI √
– 5s
– 3s √
OI √ 7h
+ 3h =
10h √
{ , }
– 2 5
{ , }
– 3
– 7 F L F L
3. 5s2 – 17s = – r = r + 3 1, 5 1, 6 1, 4 1, 3
5s2 – 17s = 0
+ 6
4r = 0
– r
– 3 2, 3 2, 2
( )( )
( )( ) 1 s – 3 5 s – + 2
= 0 4 r 3 1 r – 1
= 0
OI √
– 2s
– 15s =
– 17s √
OI √
– 4r
+ 3r =
– 1r √
{ , }
{ , } 3 1 5 4

4. White Boards OI √ – 5x – 6x = – 11x OI √ – 6x + 7x = 1x
Solving by Factoring
White Boards
OI √
– 5x
– 6x =
– 11x √
OI √
– 6x
+ 7x = 1x √

5. Solving using square roots:
Together
White Boards

6. 5.5 Quadratic Equations
(Day 2)

7. Solving by Factoring 1. 3x2 – 20x – 7 = 0 2. 2x2 + 7x – 5 = 0
White Boards
1. 3x2 – 20x – 7 = x2 + 7x – 5 = 0

8. Solving by Graphing Enter 2x2 + 7x – 5 into Y1 and graph the function.
Use a graphing calculator to solve 2x2 + 7x – 5 = 0. Round the solutions to the nearest hundredth.
Enter 2x2 + 7x – 5 into Y1 and graph the function.
Use CALC to find the two zeros.

9. Solving by Graphing 4. x2 + 3x – 6 = 0 5. 2x2 + 4x = 11 White Boards
Give your answers to at most two decimal points.
4. x2 + 3x – 6 = x2 + 4x = 11

10. Real-World Connection
The function y = -16x models the height y in feet of a heavy object x seconds after it is dropped from the top of a building that is 270 feet tall. How long does it take the object to hit the ground?

11. Real-World Connection
A carpenter wants to cut a piece of plywood in the shape of a right triangle. The carpenter wants the hypotenuse of the triangle to be 6 feet long and the legs be as shown in the diagram. About how long should the perpendicular sides be?
6 ft.
x + 1 x