Section 8.1 Quadratic Equations The Graphical Connection The Principle of Square Roots Completing...
13
Section 8.1 Quadratic Equations The Graphical Connection The Principle of Square Roots Completing the Square Solving Equations by Completing the Square Problem Solving 8.1 1
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Transcript of Section 8.1 Quadratic Equations The Graphical Connection The Principle of Square Roots Completing...
8.1 1
Section 8.1 Quadratic Equations The Graphical Connection The Principle of Square Roots Completing the Square Solving Equations by Completing the Square Problem Solving
8.1 2
Review of Quadratic Equations
.0 and
numbers real are and , , where0
writtenbecan that one isequation quadraticA 2
a
cbacbxax
In Chapter 5, we solved these types of equations by factoring the non-zero side.
When the expression is unfactorable, we need an alternate way to find solutions.
24
0)2)(4(
0862
xorx
xx
xx
?9
?2
?1243
2
2
2
x
x
xx
8.1 3
Quadratic Functions & Graphs In Chapter 2, we examined
f(x) = ax2 + bx + c a ≠ 0
8.1 4
The Principle of Square Roots
Solve by factoring
x2 – 16 = 0
Then by the square root property
44
0)4)(4(
0162
xorx
xx
x
416
16
0162
2
x
x
x
8.1 5
Solve Using the Square Root Property
23
18
18
0182
2
x
x
x
x
ix
x
x
x
23
49
492
2
1
094
510
55
52
522
2 025
x
x
x
x
8.1 6
General Form of the Principle of Square Roots - Let X be any Expression
51
3232
32
9)2( 2
xorx
xx
x
x
22
2222
22
2)2(
2)(
)2()(
2
2
x
xx
x
x
xfwhenxallfind
xxf
kXorkXthenkXIf ,2
8.1 7
What do you notice about the left expression?
It’s a perfectsquare trinomial:
23
23
2)3(
2962
2
x
x
x
xx
8.1 8
Completing the Square- A technique used to find solutions to quadratic equations
Recall the patterns for factoring “perfect square trinomials:
Add a number to x2 + 6x to make it a perfect square. 222
21 )3(969336 xxxsoand
225
4252 )(5 aaa
8.1 9
Using the Perfect Square Technique in an Equation
solutionsThexx
sidesbothofrootSqxandx
formsquareinWritex
sidesbothtovalueAddxx
sideothertotermconstMovexx
xx
2184
711711
49)11(
1217212122
7222
07222
2
2
2
2
8.1 10
Solving by Completing the Square
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267
322
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372
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372
33
2
2
)(
)()(
273
0273
x
x
x
x
xx
xx
xx
xx
8.1 11
Examples - board Solve by factoring
Use square root property
Use completing the square
8.1 12
Application – Compound Interest
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1
1
)1(
)1(
)1(40004410
)1(
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2021
2021
2
2021
2400441
2
2
2
r
r
r
r
r
r
rPA t
8.1 13
What Next? The Quadratic Formula Present Section 8.2
