Adv.Algebra 2 Ch. 2
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| What is the Standard Form formula? | f(x)=ax² + bx + c where y=0
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| What is the Factored Form formula? | f(x)=a(x-rsub1)(x-rsub2)
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| What is the Vertex Form formula? | f(x)=a(x-h)²+k
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| Standard Form: Axis of Symmetry | x=-b/2a
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| Standard Form: X-Intercept(s) | -b plus or minus the square root of b² minus 4ac, all over 2a.
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| Standard Form: Concavity | "a" value
+=opens up
-=opens down
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| Standard Form: Vertex | Use axis of symmetry to find x-coordinate, substitute into equation for x and solve for y.
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| Standard Form: Y-Intercept | The c in the Standard Form equation.
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| Factored Form: Axis of Symmetry | rsub1 + rsub2 then divided by 2
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| Factored Form: X-Intercept(s) | (rsub1,0)(rsub2,0)
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| Factored Form: Concavity | "a" value
+=opens up
-=opens down
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| Factored Form: Vertex | Use axis of symmetry to find x-coordinate, substitute into equation for x and solve for y.
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| Factored Form: Y-Intercept | Plug in x=0 and solve for y.
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| Vertex Form: Axis of Symmetry | x=h
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| Vertex Form: X-Intercept(s) | 1) Plug in y=0
2) -factor
-calculator
-quadratic formula
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| Vertex Form: Concavity | "a" value
+=opens up
-=opens down
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| Vertex Form: Vertex | (h,k)
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| Vertex Form: Y-Intercept | Plug in x=0 to find y-intercept
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| Vertical Compression | The squeezing of a graph towards the x-axis (A>OR=1)
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| Vertical Stretch | The stretching of the graph away from the x-axis(0<A<1)
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| The coordinate notation represented in y=Af(x-C)+D | (x,y) -> (x+C, Ay+D)
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| Horizontal Dilation | A type of transformation that stretches or compresses the entire graph
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| Horizontal Stretching | The stretching of a graph away from the y-axis
0<|B|<1
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| Reflection of a graph | A mirror image of a graph across its line of reflection
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| Line of reflection | The line that graph is reflected across
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| Vertical Dilation | A type of transformation that stretches or compresses an entire figure or graph
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| Horizontal Compression | The squeezing of a graph towards the y-axis
(|B|>1)
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| af(B(x-C))+D | "A" affects y (multiply)
"B" affects x "opposite" (multiply)
"C" affects x "opposite" (+/-)
"D" affects y (+/-)
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| The coordinate notation represented in y=Af(B(x-C))+D | (x,y) -> (1/B(x)+C,Ay+D)
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| 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
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| i= | i= √(-1)
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| i²= | i²= -1
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| i^3= | i^3= -√(-1)
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| i^4= | i^4= 1
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| 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
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| Pure Imaginary Number | A number of the form bi, where b is not equal to 0
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| Set of Complex Number | The set of all numbers written in the form
a+bi, where a and b are real numbers
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| Real Part of a complex Number | Term "a" for a+bi in a set of complex numbers
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| Imaginary Part of a Complex Number | Term "b" for a+bi in a set of complex numbers
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| 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
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| 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.
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| 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.
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| 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.
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| 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.
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| 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
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| Monomial | A polynomial with one term
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| Binomial | A polynomial with two terms
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| Trenomial | A polynomial with three terms
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| Discriminant | The radicand expression in the Quadratic Formula, b²-4ac
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| Fundamental Theorem of Algebra | Any polynomial equation of degree n must have exactly n complex roots or solutions
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| 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
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| y=f(x)+D -D>0 What type of Transformation? | Vertex moves up D-units
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| y=f(x)+D -D<0 What type of transformation? | Vertex moves down D-units
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| y=f(x-C) -C>0 What type of transformation? | Vertex moves to the right
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| y=f(x-C) -C<0 What type of transformation? | Vertex moves to the left
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| y=Af(x) -|A|>1 What type of transformation? | Vertical stretch
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| y=Af(x) -0<|A|<1 What type of transformation? | Vertical compression
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| y=Af(x) -A<1 What type of transformation? | Reflection across x-axis
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| y=f(Bx) -|B|>1 What type of transformation? | Horizontal compression
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| y=f(Bx) - 0<|B|<1 What type of transformation? | Horizontal stretch
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| y=f(Bx) - B<0 What type of transformation? | Reflection across y-axis
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| Translation | A type of transformation that shifts an entire figure or graph the same distance and direction
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