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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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