Download presentation

Presentation is loading. Please wait.

Published byDarnell Paylor Modified over 2 years ago

1
MATH Part 2

2
Linear Functions - Graph is a line Equation of a Line Standard form: Ax + By = C Slope Intercept Form: y = mx + b m = slope b = y – intercept or the value of y when x is zero

3
Equation of a Line

4
Slope and Orientation of Lines POSITIVE SLOPE NEGATIVE SLOPE UNDEFINE D SLOPE ZERO SLOPE

5
Parallel and Perpendicular Lines Parallel Lines Perpendicular Lines Same slope m 1 = m 2

6
x and y intercepts y - intercept - Value of y when x is zero x – intercept - Value of x when y is zero

7
Quadratic Equations Equations dealing with variables whose highest exponent is 2. Standard form: y = ax 2 + bx + c

8
Factoring Get the Common Monomial Factor first. After getting the CMF, use the techniques of factoring. Example: 12x 4 - 48x 3 - 15x 2 = 3x(4x 3 -16x 2 – 5x)

9
Trinomials Factoring where a = 1 x 2 + bx + c = (x + m)(x + n) Wherein: m + n = b mn = c

10
Example: x 2 + 3x – 10 What are the factors of c which give a sum of b? (x – 2)(x + 5) m = -2; n = 5 m + n = 3 mn = -10

11
Trinomials Factoring where a ≠ 1 ax2 + bx + c = (mx + n)(px +q) Wherein: mq +np = b nq = c

12
Example: 6x 2 – 5x – 6 = (3x + 2)(2x – 3) m = 3, n = 2, p = 2, q = -3 3(-3) + 2(2) = -5 2(-3) = -6

13
Perfect Square Trinomials x 2 + 2xy + y 2 = (x + y) 2 Example: x 2 – 8x + 16 = (x – 4) 2

14
Binomials Difference of Two Squares (DOTS) x 2 – y 2 = (x + y)(x – y) Example: 36c 2 -144 = (6c + 12)(6c – 12)

15
Sum of Two Cubes x 3 + y 3 = (x + y)(x 2 – xy +y 2 ) Example: y 3 + 8 = (y + 2)(y 2 – 2y + 4)

16
Difference of Two Cubes x 3 – y 3 = (x – y)(x 2 + xy + y 2 ) Example: b 3 – 64 = (b – 4)(b2 + 4b + 16)

17
Applications of Factoring Simplifying rational algebraic expressions or dividing polynomials Getting the solutions/roots/zeroes of quadratic equations

18
Quadratic Formula An alternative way of solving for the roots/zeroes of a quadratic equation

19
Discriminant If b 2 – 4ac < 0 - no real roots, imaginary If b 2 – 4ac = 0 - roots are real and equal If b 2 – 4ac > 0 - roots are real and unequal

20
Laws of Exponents 1

21
Exponential Functions One to One Correspondence of Exponential Functions If x a = x b Then a = b

22
Radicals

23
Rationalizing Radicals

24
Adding or Subtracting Radicals

25
Logarithmic Functions log a N = x N = a x Example: log 2 32 = 5 32 = 2 5 Common Logarithm -No indicated base base is 10 Example: Log 10,000 = log 10 10000 = 4

26
Properties of Logarithm

27
Imaginary Numbers

Similar presentations

Presentation is loading. Please wait....

OK

Factoring Polynomials.

Factoring Polynomials.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on mergers and acquisitions in banking Ppt on electronic product design Download ppt on pulse code modulation pcm Ppt on forward rate agreement currency Ppt on new zealand cultures Ppt on obesity diet management Ppt on energy conservation act 2001 Ppt on water activity in food Ppt on solar energy conversion Ppt on condition monitoring jobs