A little Pre-Calculus (Advanced Algebra and Geometry)

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Presentation transcript:

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 = y 2 – y 1 x 2 – x 1

A( 1, 4 ) B( 4, -2) x 1, y 1 x 2, y 2 m = -2 – (+4) 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 33X 91X 9 = 3 X 3

Notice: 4(x + 2) = 4x + 8 Expanding Factoring

Factor x 2 + 5x + 6 =(x )(x ) simple Add: 5 Multiply: 6

Complex: (a > 1) Decomposition Add to the middle, multiply to (first)(last) Common Factor twice

Factor 6x 2 – 1x – 2 =6x 2 – 4x + 3x – 2 = 2x(3x – 2) + 1(3x – 2) = (3x – 2)(2x + 1) You may also guess and check complex Add: -1 Multiply: -12 CF the first pair, then CF the second pair

Difference of Squares x 2 – y 2 = (x – y)(x + y) x 2 – 25 =(x – 5)(x + 5)

Expand and Simplify: (use FOIL) = x - 2

Simplify

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 = h - 2 = h

For the function f(x) = 6x, determine in simplified form = 6

Pg 2 [2,3,4] a,c 6a,c,e 8a,c 10a, 11a 12 13(use DESMOS)