Download Solving Quadratic Equations

4.5: Do Now: Simplify.
1) 24
2) 6  15
3) 150
Academy Algebra II
4.5: Solve quadratic equations by
finding the square root.
HW: p.269 (4-18 even)
Test 4.1-4.6: Friday, Oct. 3rd
(Tutorial: next week Tues and Thurs)
Product and Quotient
Property
• Product Property
xy 
x
• Quotient Property
x

y
x
y
y
Ex of the Product & Quotient Property
Simplify the following:
1)5 24  3 10
11
2)
25
9
3)
64
Rationalizing the
Denominator
• Can never have a radical in the denominator of
a fraction.
 You must rationalize the denominator.
2
7

2
2
Examples of Rationalizing the
Denominator
25
1)
3
18
2)
22
Conjugates
• The conjugate of 3  7 is 3  7
• We can use conjugates to simplify
expressions (by rationalizing the
denominator) like:
• Multiply the numerator and denominator
by the conjugate of the denominator.
2
3 7
3 7

3 7
Simplify by rationalizing
the denominator:
4
1.)
6  20
Academy Algebra II
4.5: Solve quadratic equations by
finding the square root.
HW: p.270 (22-34 even)
Test 4.1-4.6: Friday, Oct. 3rd
(Tutorial: next week Tues and Thurs)
Simplify by rationalizing
the denominator:
5

3
2.)
2 6
Solving Quadratic Equations
Solve: x  64
(Take square root of both sides)
2
x   64
x  8
Solving Quadratic Equations
Solve:
2
1.) 4 x
 64
2.)
1 2
x 8
3
Solving Quadratic Equations
Solve:
2
3.) 2 x
4.)
 5  81
( x  8)  12  13
2
Solving Quadratic Equations
Solve:
2
5.) 2( x  3)
 7  43
Solving Quadratic Equations
Solve:
1
2
6.)
(3x)
2
 6  52