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# Algebra 2

### Semester 1 final

Natural Numbers Counting numbers(1,2,3,4)
Whole Numbers Add Zero
Integer Numbers Adding negatives
Rational Numbers Add Fractions
Real Numbers Any number
Opposite(Additive Inverse) Number add to original number to equal zero
Reciprocals( Multiplicative Inverse) Get 1 for an answer
Closure Property A+b is a real #, ab is a real #
Commutative Property a+b= b+a
Associative Property (a+b) + c= a + (b+c), (ab)c= a(bc)
Identity Property a+ 0 =a, a* 1= 1
Inverse Property a+(-a)=0, a*1/a= 1
Distributive Property a(b+c)= ab+ac
Relation Set of pairs of input and output values
Domain Set of all inputs(x-values)
Range Set of all outputs(y-values)
Function Relation which each input has exactly one output
Vertical Line Test If a vertical line passes through 2 or more points on a graph then the relation is not a function
Linear Equation First degree equation
Linear Function Function graph is in a line
Slope- Intercept Form y=mx+b
Point- Slope Form y-y1=m(x-x1)
Standard Form Ax+By=c
X intercept y=0
Y intercept x=0
Hoy Horizontal, 0 slope, equation is y=#
Vux Vertical, undefined slope, equation is x=#
Independent Solution Has one solution
Dependent Solution Infinite Solutions
Inconsistent Solution No solution
Same slope, same y int. Dependent
Same slopes, diff y int. Inconsistent
Different slopes, different y int. Independent
Substitution Solve 1 equation for 1 of variables. Substitute equation into other equation and solve. Substitute answer into one of the original equations.
Elimination Method Line up variables and constants. Make coefficients of 1 variables opposites by multiplying entire equation by something. Add 2 equations together. Solve for left over variable. Substitute.
Elimination with 3 Equations Use 2 equations to eliminate 1 variable. Use 2 other equations the same variable. Use 2 new equations with 2 variables to solve like before.
Sin Opposite/Hypotenuse
Csc Hypotenuse/Opposite
Zero Matrix All elements equal 0(Identity property of addition)
Opposite Matrix Added to original Inverse Property of Addition
Equal Matrices Matrices with same dimensions and equal corresponding elements, when simplified
Quadratic Function(Standard Form) f(x)= ax^2+bx+c
Parabola Graph of quadratic.
Axis of Symmetry Vertical line that divides a parabola into 2 parts mirror images
Vertex point parabola intersects axis of symmetry
Y-Coordinate is either the min. or max. of the function
Vertex Form y=a(x-h)^2 +K
The Discriminant Equation in form ax^2+bx+c=0 value of b2-4ac
Created by: tatummilo333