# Math Final

version from 2018-05-05 22:24

## Section 1

Standard form of a quadratic functionF(x)=ax2+bx+c
Standard form of a quadratic equation ax2+bx+c=0
Axis of symmetry x=-b/2a
Vertex formulaf(x)=a(x-h)2+k
Slope Intercept Formy=mx+b
Slopem=y2-y1/x2-x1
Standard Formax+by=c
Point Slope Formy-y1=m(x-x1)
Three Ways to Solve a System of Linear Equationsgraphing, substitution, addition/elimination
Three Types of Systems for Two Linear Equationsconsistent (2 lines intersect, 1 solution), inconsistent (parallel, no solution), dependent (lines are the same, infinite solutions)
Polynomial Product Rulex2*x3 - same base, combine the base and add the exponents
Quocient Ruleif the bases are the same, subtract
Power Rule(xy)2 = x2y2
Negative Exponent Rulex-1 = 1/x
Quocient Power Rule(2/x)3=(2)3/(x)3=2^3/x^3=8/x3
Negative Exponent Power Rule(2/x)-3 = (x/2)3
Monomialone term
Binomialtwo terms, terms are separated by + or -
Trinomialthree terms
When Adding or Subtracting Polynomialscombine like terms (same variable, raised to the same power)

## Section 2

Simplification of Exponential Expressionsno negative exponents remain, no duplicate variables remain, simplify any fractions if possible
Factoring Polynomialslook for GCF, use grouping (4 terms) a^2b=ab^2+ab - GCF is ab - ab(a+b+1)
Trinomialax2+bx+c --- find two factors of c whose sum is equal to b, a trinomal usually factors into two binomials
Trinomials ContB+C+ both factors +, B-C+ both factors -, B+C- 1 factor is + the other is -, B-C- 1 factor is + the other is -
Area of a Rectanglel*w=a
To add or subtract rational expressions with unlike denominators we mustfind LCM of denominators, form equivalent fractions, perform the indicated operation
To solve a rational equationfind LCD, multiply by all terms in the equation by LCD, solve
Extraneous Solutionrational equations sometimes don't have a solution because the solution makes a denominator 0
Perimeter Equation2L+2W=P
Functiona function is the relationship between the input x and the output f(x) -- f(x)=y
Absolute Valuethe distance from 0 l-2l would be 2, can never be negative

## Section 3

Pefect Squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Perfect Cubes1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Perfect 4ths1, 16, 81
Perfect 5ths1, 32, 243
To multiply radical expressionsmust have same index, simplify
A simplified radical expressionno perfect power of the index remains in the radicand, no fraction remains under the radical sign, no radical remains in a denominator
Radical Equationsisolate one radical and left hand side and solve, always check for extraneous solutions
Pythagreon Theruma2+b2=c2
Standard Form of a Quadratic Functionf(x)=ax2+bx+c
Standard Form of a Quadratic Equationax2+bx+c=0
In Order to Graph a Quadratic Equationup or down, find axis of sym, vertex, find y int, find x int
Vertex Formf(x)=a(x-h)2+k
Ways to Solve a Quadratic Equationfactoring, square root property, complete the square, quadratic formula, substitution
How to CTSdivide all terms by "a" (the coefficient of x2), move the number term (c/a) to the right side of the equation, complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation