Algebra II Honors POD
Homework: p. 102 1-11 odds, 13-23 odds
(you must use completing the square), and 77, 83
Find all real solutions for the following:
a) x  3x  3  0
b) x 1  0
2
c) x  5x  2  0
d) x  4   0
2

a) x  3, 3
b) no real solution
c) x 5, 2
d) x  4
Quadratic equations have the form:
y  ax  bx  c
2
In the equation a, b and c are real and a ≠ 0.

The roots of a quadratic equation are the x values
that make the y value equal zero.
Zero-Product Property
AB = 0 if and only if A = 0 or B = 0.
Match each equation to its graph on the board.
a) y  x 2 1
b) y  x 2  3x 10
c) y  x 2  9
d) y  x 2  8x 16
Completing the Square
x  3  7
x 2  278
2
x   278


x3 7
x  3 7

x 2  8x  7  0 
x  7x 1  0
x  7, 1




Let’s solve

x 2  8x  7  0
x 2  8x
another way.
 7
x 2  8x 16   7 16

x  4  9
2
x4  9

x  43

x  7, 1


Completing the square for
ax 2  bx  c  0
1) Subtract c.
2) Divide by a.
3)
4)
5)
6)

2


1
b
Add    to both sides of the equation.
2 a 
Factor.
Take the square root of both sides.
Solve for x.
Even answers from page 102.

14) 2  2
20) 1 or 19
1
7
16) or 
2
2
5
21
18) 
2
2
2 3
22) 1
3
1
1
24) or
2
4
Algebra II H POD
Homework: p. 102 25-59 odds, 69, 71, 82
Solve the following by completing the square.
ax 2  bx  c  0

b  b 2  4ac
x
2a
This is called the Quadratic Formula.

Any quadratic
equation can be solved using this formula.

Solve


5x 2 13x  6  0
using the quadratic formula.
b  b 2  4ac
x
2a
13 132  (4)(5)(6)
x

2(5)
x
13 169 120
10




a  5, b 13, c  6
x
13 289
10
1317
x
10
2
x , 3
5
b  b 2  4ac
x
2a

Opposite of b, Opposite of b
Plus or minus square root, Plus or minus square root
b squared minus 4ac, b squared minus 4ac
Over 2a, Over 2a