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# Adv.Algebra 2 Ch. 2

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

What is the Standard Form formula? | f(x)=ax² + bx + c where y=0 |

What is the Factored Form formula? | f(x)=a(x-rsub1)(x-rsub2) |

What is the Vertex Form formula? | f(x)=a(x-h)²+k |

Standard Form: Axis of Symmetry | x=-b/2a |

Standard Form: X-Intercept(s) | -b plus or minus the square root of b² minus 4ac, all over 2a. |

Standard Form: Concavity | "a" value +=opens up -=opens down |

Standard Form: Vertex | Use axis of symmetry to find x-coordinate, substitute into equation for x and solve for y. |

Standard Form: Y-Intercept | The c in the Standard Form equation. |

Factored Form: Axis of Symmetry | rsub1 + rsub2 then divided by 2 |

Factored Form: X-Intercept(s) | (rsub1,0)(rsub2,0) |

Factored Form: Concavity | "a" value +=opens up -=opens down |

Factored Form: Vertex | Use axis of symmetry to find x-coordinate, substitute into equation for x and solve for y. |

Factored Form: Y-Intercept | Plug in x=0 and solve for y. |

Vertex Form: Axis of Symmetry | x=h |

Vertex Form: X-Intercept(s) | 1) Plug in y=0 2) -factor -calculator -quadratic formula |

Vertex Form: Concavity | "a" value +=opens up -=opens down |

Vertex Form: Vertex | (h,k) |

Vertex Form: Y-Intercept | Plug in x=0 to find y-intercept |

Vertical Compression | The squeezing of a graph towards the x-axis (A>OR=1) |

Vertical Stretch | The stretching of the graph away from the x-axis(0<A<1) |

The coordinate notation represented in y=Af(x-C)+D | (x,y) -> (x+C, Ay+D) |

Horizontal Dilation | A type of transformation that stretches or compresses the entire graph |

Horizontal Stretching | The stretching of a graph away from the y-axis 0<|B|<1 |

Reflection of a graph | A mirror image of a graph across its line of reflection |

Line of reflection | The line that graph is reflected across |

Vertical Dilation | A type of transformation that stretches or compresses an entire figure or graph |

Horizontal Compression | The squeezing of a graph towards the y-axis (|B|>1) |

af(B(x-C))+D | "A" affects y (multiply) "B" affects x "opposite" (multiply) "C" affects x "opposite" (+/-) "D" affects y (+/-) |

The coordinate notation represented in y=Af(B(x-C))+D | (x,y) -> (1/B(x)+C,Ay+D) |

Imaginary Number i | A number such that i²= -1. No real number exists such that its square is equal to a negative number, the number "i" is not a part of the real number system |

i= | i= √(-1) |

i²= | i²= -1 |

i^3= | i^3= -√(-1) |

i^4= | i^4= 1 |

Set of Imaginary Numbers | The set of all numbers written in the form a+bi, where a and b are real numbers and b is not equal to 0 |

Pure Imaginary Number | A number of the form bi, where b is not equal to 0 |

Set of Complex Number | The set of all numbers written in the form a+bi, where a and b are real numbers |

Real Part of a complex Number | Term "a" for a+bi in a set of complex numbers |

Imaginary Part of a Complex Number | Term "b" for a+bi in a set of complex numbers |

If a number is an imaginary number, then it is _____ a complex number. -Always -Sometimes -Never | If a number is an imaginary number, the it is always a complex number |

If a number is a complex number, then it is _____ an imaginary number. -Always -Sometimes -Never | If a number is a complex number, then it it sometimes an imaginary number. |

If a number is a real number, then it is ____ a complex number. -Always -Sometimes -Never | If a number is a real number, then it is always a complex number. |

If a number is a real number, then it is ____ an imaginary number. -Always -Sometimes -Never | If a number is a real number, then it is never an imaginary number. |

If a number is a complex number, then it is ____ a real number. -Always -Sometimes -Never | If a number is a complex number, then it is sometimes a real number. |

Complex Conjugates | Pairs of numbers of the form a+bi and a-bi. The product of a pair of complex conjugates is always a real number and equal to a²+b² |

Monomial | A polynomial with one term |

Binomial | A polynomial with two terms |

Trenomial | A polynomial with three terms |

Discriminant | The radicand expression in the Quadratic Formula, b²-4ac |

Fundamental Theorem of Algebra | Any polynomial equation of degree n must have exactly n complex roots or solutions |

Double roots | The 2 real roots, ex.: If the graph of a quadratic function f(x) has 1 x-intercept, the equation f(x)=0 still has 2 real roots |

y=f(x)+D -D>0 What type of Transformation? | Vertex moves up D-units |

y=f(x)+D -D<0 What type of transformation? | Vertex moves down D-units |

y=f(x-C) -C>0 What type of transformation? | Vertex moves to the right |

y=f(x-C) -C<0 What type of transformation? | Vertex moves to the left |

y=Af(x) -|A|>1 What type of transformation? | Vertical stretch |

y=Af(x) -0<|A|<1 What type of transformation? | Vertical compression |

y=Af(x) -A<1 What type of transformation? | Reflection across x-axis |

y=f(Bx) -|B|>1 What type of transformation? | Horizontal compression |

y=f(Bx) - 0<|B|<1 What type of transformation? | Horizontal stretch |

y=f(Bx) - B<0 What type of transformation? | Reflection across y-axis |

Translation | A type of transformation that shifts an entire figure or graph the same distance and direction |

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