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46 Cards in this Set
- Front
- Back
- 3rd side (hint)
Parent Function: Linear
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y=f(x)= x
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Parent Function: Quadratic
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y=f(x)=x^2
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Parent Function: Cubic
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y=f(x)=x^3
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Parent Function: Square Root
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y=f(x)=□x
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Slope Intercept Form
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y=mx+b
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Point- Slope Form
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m=y2-y1/x2-x1
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Horizontal Reflection: f(x)
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f(-x)
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Vertical Reflection: f(x)
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-f(x)
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Horizontal Compression/Stretch: f(x)
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f(1/b x)
Flip and put inside |
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Vertical Compression/Stretch: f(x)
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a×f(x)
Put on outside |
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Interpolation
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making a prediction with x value inside domain
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on the line
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Extrapolation
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making a prediction with x value outide domain
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off the line
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Methods for Solving Linear Systems
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Graphing, Substitution, Elimination
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3 methods
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Vertex Form
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f(x)=a×(x-h)^2+k
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Standard Form
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y=ax^2+bx+c
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Intercept/Factored Form
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y=a(x-P)(x-q)
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A.O.S.
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x=-b/2a
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A.O.S.=x
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Complete the Square
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(b/2)^2
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formula
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Values of I, I^2, I^3, I^4
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i=□-1
i^2=-1 i^3=-i i^4=1 find nearest multiple then count to nearest goes counterclockwise |
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Methods for Solving Quadratic Equations
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quadratic formula, conpleting the square, square roots, graphing, factoring, difference of two squares, GCF
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7 methods
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Complex Numbers
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a+bi
3+2i |
formula and example
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Quadratic Formula
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x=-b+- □b^2-4ac
2a |
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Discriminant
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b^2 -4ac
D>0 = 2 real D=0 = 1 real (Vertex) D<0 = 2 nonreal |
formula and number of roots
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Complex Conjugate
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i multiplied by -1
answer becomes real number |
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Pythagorean Theorum: Distance From Origin to Point
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|z|= □a^2+b^2
Ex: 2+2i a=2 b=2 |
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Steps to Solve Quadratic Inequalities
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1) Move all to one side, set equal to zero, and factor
2) Plot roots on number line and identity intervals 3) Plug in point from each to identity solution |
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<,> in Graphs
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dotted graph
open circle (parentheses) x<2= shade inside x>2= shade outside |
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<_, >_ in Graphs
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solid graph
closed circle [brackets] x<2= shade inside x>2= shade outside |
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Add/Subtract Polynomials
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combine like terms
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Pascals Triangle
0-5 |
1
1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 |
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SOAP
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Same ,Opposite, AlwaysPositive
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Sum of Cubes
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a^3+b^3
(a+b)(a^2-ab+b^2) SOAP |
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Difference of Cubes
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a^3-b^3
(a-b)(a^2+ab+b^2) SOAP |
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End Behavior
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Sketching Roots of a Graph
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x^1= cross
x^2,4,6,8= bounce x^3,5,7,9= cross with twist |
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Rational Root Theorum
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c/a= factors/factors
Test factors with synthetic division until remainder is 0 |
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Multiplicity
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repeated solutions
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Volume
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l×w×h
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Standard Form Circle
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(x-h)^2 + (y-k)^2 =r^2
(h,k) is center |
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Distance Formula
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Direct/Inverse Variation
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Direct- y=ax (linear)
Indirect- y=a/x (hyperbola) |
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Rational Function
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y=a/x-h + k
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H.A./V.A.
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H.A.=y=k
V.A.=x=h |
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Standard Form for Equation of a Parabola
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Steps to Graph Rational Functions
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1) Find H.A.
2) Find V.A. 3) Graph asymptotes and find 2 reference points 4) Sketch/graph |
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Holes
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Values of x crossed out after factoring
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