2. Pre-Calculus (Advanced Algebra and Geometry)

3. We are going to begin our work with linear and quadratic functions

4. More specifically, their intersections are very interesting to us…

5. The slope of a straight line measures the steepness of that line (km measure distance Kg measure mass…) Linear:

6. 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

7. 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

8. Graph the following quadratic y = x 2 + 3x + 5 xy FD -4 -3 -2 0 1 2 9 5 3 3 5 9 15 2D - 4 2 0 -2 -4 -6 - 2 2 2 2 2 Draw in sketchpad…. quadratic:

9. 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:

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

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

12. 3x + 6 3 sub = 2 Direct = 3(2) + 6 3 = 12 3 = 4 Factoring 3x + 6 3 = 3(x + 2) 3 1 1 = x + 2 = 4

13. Crossing out 3x + 6 3 = x + 6 = 8

14. Trinomials: ax 2 + bx + c Simple (a = 1): Add to the middle Multiply to the last

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

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

17. 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

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

19. Rationalize the denominator: X

20. Expand and Simplify: X-2

21. Simplify

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

23. For the function f(x) = 6x – 2, determine f(3 + h) in simplified form 6h + 16

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

25. See sheet 2,3,4,6,8,9, 10,11,12