# Solving Equations

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Algebra2 LB5

y-y1=m(x-x1)

Ax+Bx=C

(-b/m,c)

### Relation

Set of pairs of input and output values

### Domain

Set of inputs (x- value)

### Range

Set of outputs (y-value)

### Function

Relation in which one element of domain is paired with EXACTLY one element in range

### Vertical Line Test

If passes 2 points on graph=> NOT a function

### Coinciding Lines

Same Line ( All Real )

ParallelI

### Independent Lines

Have one solution; Different slopes

### Subsitution

Solving for one variable in one equation & plugging it into the second

### Elimination- Linear Combination

Add equations together to eliminate a variable

f(x)=ax2+bx+c

f(x)=x+c

### Vertex of a Quadratic Function

(-b/2a, Plug it in)

y=a(x-h)2+k

A2-B2=(A-B)(A+B)

### Difference of 2 Cubes

A3-B3=(A-B)(A2+AB+B2)

### Sum of 2 Cubes

A3+B3=(A+B)(A2-AB+B2)

### Discriminant

(Square root of) b2-4ac

Example: