Algebra A

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Algebra A

Chapter 2 Expression

Term: The product of a constant and a variable raised to some power.

Others

420x^5+69x^4+420x^3-69x^2+420x

Polynomial: Four Terms

69x^4+420x^3-69x^2+420x

Trinomial: Three Term

420x^3-69x^2+420x

Binomial: Two Terms

69x^2-420x

Coefficients: Constant(numbers that never change)

69 and 420

Variables: Letters

X, Y

Chapter 3 Equations

Quadratic Equation

Solving Quadratics

(-b±√(b²-4ac))/(2a)

Factoring

General Quadratics

Monic Quadratics

When we turn x^2+bx+c to (x+r)(x+s), we need to use r+s=b rs=c

Vertex: A point where two curves meet

Shapes

a<0

Facing down

a=0

Line

a>0

Facing up

Roots

Vieta's Formula

x1+x2=-b/a; x1x2=c/a

Intercept Formula: Discriminant b2-4ac

Negative

Positive

Quadratic Formula

Factored

f(x)=a(x-r)(x-s)

A(x-h)^2+K

General

Ax^2+Bx+C=0

Linear Equation

Slope

Shape

Undefined: The line is vertical

0: The line is horizontal

Negative: The line goes downward as it goes from left to right.

Positive: The line goes upward as it goes from left to right

Relationship

Perpendicular: m1m2=-1

Parallel m1=m2

Undefined

Formula

(y1-y2)/(x1-x2)

Graphing

Distance

√[(x₂ - x₁)² + (y₂ - y₁)²]

Mid-Point

[(x)1 + (x)2]/2, [(y)1 + (y)2]/2

Linear Formulas

Horizontal

y=b

Vertical

x=a

Standard Form

Ax+By=C

Point-Slope Formula

y-y1=x(x-x1)

Slope-Intercept Formula

y=mx+b

Chapter 1 Numbers

Rational Numbers: Numbers that can be written as a fraction

integers

Negative Integers -420

Whole Numbers 69

Zero

Natural Number/Positive Integer

Prime Number 7

Composite Number(number that can be divisible by more than just itself and 1) Example: 69

1

Non integers

Mixed Units 69^(69/420)

Fractions 69/420

Decimals 69.420

Irrational Numbers: Numbers that cant be written as a fraction

sqrt69

π