# Math Final

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2018-05-05 22:24

## Section 1

Question | Answer |
---|---|

Standard form of a quadratic function | F(x)=ax2+bx+c |

Standard form of a quadratic equation | ax2+bx+c=0 |

Axis of symmetry | x=-b/2a |

Vertex formula | f(x)=a(x-h)2+k |

Slope Intercept Form | y=mx+b |

Slope | m=y2-y1/x2-x1 |

Standard Form | ax+by=c |

Point Slope Form | y-y1=m(x-x1) |

Three Ways to Solve a System of Linear Equations | graphing, substitution, addition/elimination |

Three Types of Systems for Two Linear Equations | consistent (2 lines intersect, 1 solution), inconsistent (parallel, no solution), dependent (lines are the same, infinite solutions) |

Polynomial Product Rule | x2*x3 - same base, combine the base and add the exponents |

Quocient Rule | if the bases are the same, subtract |

Power Rule | (xy)2 = x2y2 |

Negative Exponent Rule | x-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 |

Monomial | one term |

Binomial | two terms, terms are separated by + or - |

Trinomial | three terms |

When Adding or Subtracting Polynomials | combine like terms (same variable, raised to the same power) |

## Section 2

Question | Answer |
---|---|

Simplification of Exponential Expressions | no negative exponents remain, no duplicate variables remain, simplify any fractions if possible |

Factoring Polynomials | look for GCF, use grouping (4 terms) a^2b=ab^2+ab - GCF is ab - ab(a+b+1) |

Trinomial | ax2+bx+c --- find two factors of c whose sum is equal to b, a trinomal usually factors into two binomials |

Trinomials Cont | B+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 Rectangle | l*w=a |

To add or subtract rational expressions with unlike denominators we must | find LCM of denominators, form equivalent fractions, perform the indicated operation |

To solve a rational equation | find LCD, multiply by all terms in the equation by LCD, solve |

Extraneous Solution | rational equations sometimes don't have a solution because the solution makes a denominator 0 |

Perimeter Equation | 2L+2W=P |

Function | a function is the relationship between the input x and the output f(x) -- f(x)=y |

Absolute Value | the distance from 0 l-2l would be 2, can never be negative |

## Section 3

Question | Answer |
---|---|

Pefect Squares | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 |

Perfect Cubes | 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 |

Perfect 4ths | 1, 16, 81 |

Perfect 5ths | 1, 32, 243 |

To multiply radical expressions | must have same index, simplify |

A simplified radical expression | no perfect power of the index remains in the radicand, no fraction remains under the radical sign, no radical remains in a denominator |

To add or subtract radical expressions | we must have "like" radicals, same index, same radicand, add or subtract using coefficients |

Radical Equations | isolate one radical and left hand side and solve, always check for extraneous solutions |

Pythagreon Therum | a2+b2=c2 |

Standard Form of a Quadratic Function | f(x)=ax2+bx+c |

Standard Form of a Quadratic Equation | ax2+bx+c=0 |

In Order to Graph a Quadratic Equation | up or down, find axis of sym, vertex, find y int, find x int |

Vertex Form | f(x)=a(x-h)2+k |

Ways to Solve a Quadratic Equation | factoring, square root property, complete the square, quadratic formula, substitution |

How to CTS | divide 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 |

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