Post on 06-Jan-2018
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General Form General Form of a of a
Quadratic EquationQuadratic Equation
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