A little Pre-Calculus(Advanced Algebra and Geometry)

The slope of a straight line measures the steepness of that line.

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

A( 1, 4 ) B( 4, -2)x1, y1 x2, y2

m = -2 – (+4)

4 - 1

m = -6

3

m = -2

y = -2x + b

4 = -2(1) + b

4 = -2 + b

b = 6

y = -2x + 6

To factor an expression means to:

re-write it as a product

Why factor?

Once an expression has been factored, equivalent factors can divide to one

Mechanics:

Remember factor trees?

9

3 3X

9 1X

9 = 3 X 3

Notice:

4(x + 2) = 4x + 8

Expanding

Factoring

Factorx2 + 5x + 6 = (x )(x ) + 2 + 3

simple

Add: 5 Multiply: 6

Complex: (a > 1) Decomposition

Add to the middle, multiply to (first)(last)

Common Factor twice

Factor

6x2 – 1x – 2 = 6x2 – 4x + 3x – 2

= 2x(3x – 2) + 1(3x – 2)

= (3x – 2)(2x + 1)

You may also guess and check

complexAdd: -1 Multiply: -12CF the first pair, then CF the second pair

Difference of Squares

x2 – y2 = (x – y)(x + y)

x2 – 25 = (x – 5)(x + 5)

Expand and Simplify: (use FOIL)

)2)(2( xx

222 xxx

= x - 2

Simplify 21

21 h

)2(2 h

h

)2(2

1)2(

)2(2

)1(2

h

h

h

)2(2

22

h

h

For the function f(x) = 3x + 12, determine f(-2)

f(-2) = 3(-2) + 12

f(-2) = 6

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

f(3 + h) = 6(3 + h) - 2

= 18 + 6h - 2

= 16 + 6h

For the function f(x) = 6x , determine

h

fhf )2()2(

h

h )2(6)2(6

in simplified form

= 6

h

h 12612

Pg 2

[2,3,4] a,c6a,c,e8a,c10a, 11a1213(use

DESMOS)