PreCalculus Advanced Algebra and Geometry

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Pre-Calculus(Advanced Algebra and Geometry)
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We are going to begin our work with linear and
quadratic functions
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More specifically, their intersections are very
interesting to us
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Linear

• The slope of a straight line measures the
  steepness of that line
• (km measure distance
• Kg measure mass)

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Write the equation of the line that passes
through the points A (1,4) and B (4, -2)y mx
b

• First find the slope

m y2 y1
x2 x1
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• A( 1, 4 ) B( 4, -2)

x1, y1 x2, y2
m -2 (4)
y -2x b
4 - 1
4 -2(1) b
m -6
4 -2 b
3
b 6
m -2
y -2x 6
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Graph the following quadraticy x2 3x 5
quadratic

• x

y
FD
2D
-4
9
-
Draw in sketchpad.
-3
5
4
-
-2
3
2
2
-1
3
0
2
0
5
-2
2
1
9
-4
2
2
15
-6
2
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To factor an expression means to
Mechanics

• re-write it as a product

Why factor?
Once an expression has been factored, equivalent
factors can divide to one
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Remember factor trees?
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3
3
X
9
1
X
9 3 X 3
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Notice
Expanding

• 4(x 2) 4x 8

Factoring
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3x 6
Direct
Factoring
3x 6
3
3
3(x 2)
1
3(2) 6
sub 2
3
3
1
x 2
12
3
4
4
12
Crossing out
3x 6
3
x 6
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VERY, VERY, BAD!!
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Trinomials ax2 bx c

• Simple (a 1)
• Add to the middle
• Multiply to the last

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Factor

• x2 5x 6

(x )(x )
2 3
simple
Add 5 Multiply 6
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Complex (a gt 1) Decomposition Add to the
middle, multiply to (first)(last) Common Factor
twice
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Factor

• 6x2 1x 2

6x2 4x 3x 2
complex
Add -1 Multiply -12
CF the first pair, then CF the second pair
2x(3x 2) 1(3x 2)
(3x 2)(2x 1)
You may also guess and check
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Difference of Squares
(x y)(x y)

• x2 y2

x2 25
(x 5)(x 5)
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• Rationalize the denominator

X
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• Expand and Simplify

X-2
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Simplify
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For the function f(x) 3x 12, determine f(-2)

• (-2,6)

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For the function f(x) 6x 2, determine f(3
h) in simplified form

• 6h 16

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For the function, determine
in simplified form
f(x) 6x
6
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• See sheet
• 2,3,4,6,8,9,10,11,12