MATH Part 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

Equation of a Line

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Laws of Exponents 1

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

Radicals

Rationalizing Radicals

Adding or Subtracting Radicals

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 = 4

Properties of Logarithm

Imaginary Numbers