2. A little Pre-Calculus (Advanced Algebra and Geometry)

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

4. 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

5. A( 1, 4 ) B( 4, -2) x 1, y 1 x 2, y 2 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

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:

7. Remember factor trees? 9 33X 91X 9 = 3 X 3

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

9. Factor x 2 + 5x + 6 =(x )(x ) + 2 + 3 simple Add: 5 Multiply: 6

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

11. 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

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

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

14. Simplify

15. For the function f(x) = 3x + 12, determine f(-2) f(-2) = 3(-2) + 12 f(-2) = 6

16. 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

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

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