Transcript Solving Quadratic Equations

4.5: Do Now: Review 4.3/4.4.
The area of a rectangle with length = 3x + 1
and width = 2x + 1 is 22. Write and solve an
equation to find the dimension of the rectangle.
Algebra II
4.5: Solve quadratic equations by
finding the square root.
HW: p.269 (4-14 even), p.1013 (29-31 all)
Quiz 4.5, 4.7 (and word problems):
Tuesday, Oct. 28th
Simplify.
1) 24
2) 6  15
Product and Quotient
Property
• Product Property
xy 
x
• Quotient Property
x

y
x
y
y
Simplify.
3) 150
11
4)
25
Extra Practice: Simplify.
5)5 24  3 10
9
6)
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:
4
1)
6  20
5 3
2)
2 6
4.5: Do Now: Review 4.3/4.4
Friday’s HW: p.269 (4-14 even), p.1013 (29-31)
The product of two consecutive numbers is
210. Write and solve an equation to find the
two numbers.
Algebra II
4.5: Solve quadratic equations by
finding the square root.
HW: p.269-270 (14-34 even)
Quiz 4.5, 4.7 (and word problems):
Wednesday, Oct. 29th
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