algebra 2. graph the quadratic equation. vertex: (-3, 4) axis of symmetry: x = -3
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Algebra 2
5.3 – Solving Quadratics by Square Roots
Graph the quadratic equation.
Warm-Up
21( 3) 42
y x
Vertex: (-3, 4)Axis of symmetry: x = -3
Simplify radical expressionsRationalize the denominatorSolve quadratic equations
Objectives:
Product Property:
Quotient Property:
Square Root Properties
a b ab
a a
b b
1. No fractions in square roots
2. No perfect squares in the radical
3. No radicals in the denominator
The NO-NO’s of Square Roots
Did you know…?That it is against the law in 32 states (including Illinois)
to leave a radical in the denominator of a fraction.
Steps:1. Use a “factor
tree” to factor completely
2. Circle pairs of the same number (they go out)
3. Any other factors not part of a pair stay in
Product Property
500
100 5
10 10
2 5 52
2 5 5 10 5
Steps:1. Use a “factor tree” to
factor completely2. Circle pairs of the same
number (they go out)3. Any other factors not
part of a pair stay in
Product Property
1)
2)
3)
3 12 6
3 12
15 6 3 10
18 2
6
Steps:1. Split up into two
square root problems
2. Simplify the numerator and denominator
3. Remember the “NO-NO” rules
Quotient Property
64
9
64
9
8
3
Steps:1. Split up into two
square root problems
2. Simplify the numerator and denominator
3. Remember the “NO-NO” rules
Quotient Property25
3
25
3
25 3
3 3
5 3
3
Steps:1. Split up into two
square root problems
2. Simplify the numerator and denominator
3. Remember the “NO-NO” rules
Quotient Property
1)
2)
2
1122
11
18
362
2
Steps:1. Isolate the variable2. Include both answers
Solving a Quadratic Equation
1)
2)
22 1 17x 2 2x
21( 5) 73x 5 21x
Note: This method only works when there is no “b” term!
Steps:1. Isolate the variable2. Include both answers
Solving a Quadratic Equation
3)
4)
23 108x 6x
2
6 48
x 4 5x
pg. 267 #32-34, 38, 41, 49, 54-57, 60
Quiz on Tuesday, November 20th
Homework/Reminders:
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