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Adv.Algebra 2 Ch. 2

QuestionAnswer
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
Created by: 100000053823420