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Graphing Quadratic Equations. General Form of a Quadratic Equation. y = ax 2 + bx + c. Standard Form. ax 2 + bx + c = 0. Factoring and Solving. Rule 1 (the only rule) Find the G.C.F. Otherwise, look for something familiar. If factoring does not seem to be working…. - PowerPoint PPT Presentation

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General Form General Form of a of a

y = ax2 + bx + c

Standard Form

ax2 + bx + c = 0

Factoring and Solving• Rule 1 (the only rule)

– Find the G.C.F.– Otherwise, look for

something familiar

010112 xx

092 x

025102 xx

If factoring does not seem to be working…..

• Ask the following question:• “Is the linear term missing?”• If so, SQUARE ROOTS SEEM

GOOD.

052 x

Square Root Method• If you take the

square root of both sides of an equation, then you must get TWO answers.

39

92

2

xx

x

PERFECT SQUARED TRINOMIALS

• “FIRST TERM SQUARED PLUS TWICE THE FIRST TIMES THE LAST PLUS THE LAST TERM SQUARED.”

• Can be factored from a memorized formula.

222 )(2 bababa

Differences of Squares

• A difference of two squares can be factored.• Remember that the inner and outer terms

must be opposites.

))((22 bababa

A manufacturer determines that the number of drills it can sell is given by the formula where p is the price of the drills in dollars.

2851563 2 ppD

a. At what price will the manufacturer sell the maximum number of drills?

b. What is the maximum number of drills that can be sold?

Factor the expression.

xx 1410 2

)75(2 xx

102510 2 xx

)2)(12(5)252(5 2

xxxx

)6)(95(54215 2

xx

xx

254016 2 xx

2)54( x

4916 2 x

)74)(74( xx

Solve by factoring.

0320)7)(32(021112

0)21112(2

042224

2

2

2

xxxxx

xx

xx

07 xor

Solve the equation by finding square roots

87

644912898

98128

2

2

2

x

x

x

x

Solve the equation.

ixx

x

x

x

x

1

1

01

0)1(16

01616

2

2

2

2

Solve the equation.

414

5959

25)9(

2581182

2

xxxxx

xx

Solve by completing the square.

54

54

5)4(

1611168

0118

2

2

2

x

x

x

xx

xx

Solve by completing the square.

3649

3684)

67(

3649

37)

3649

37(

37)

37(

7)37(3

773

2

2

2

2

2

x

xx

xx

xx

xx

635

67

3635)

67(

3635)

67( 2

x

x

x

Rewrite in Vertex Form

2)5(

25232510

2310

2

2

2

xy

xxy

xxy

Rewrite in Vertex Form

7)25(53

375382)62550(53

3823053

2

2

2

xy

xxy

xxy