Algebra II

Equation of a line with the slope and y intersection

y = mx + c

What does c stand for (equation of a line)?

y-intersect

What does m stand for (equation of a line)?

Slope

How to solve three way simultaneous equations?

Cancel out one letter in each equation. After being left with two variables in two equations solve as normal and sub in.

How to get the factors when given the roots?

Change the sign of the number

What is the maximum number of distinct roots a polynomial can have?

Same as its degree

What is multiplicity?

When a polynomial has a root that occurs multiple times

Multiplicity of 1 diagram

x = -2

Multiplicity of 2 diagram

(x+1)²

Multiplicity of 3 diagram

(x+2)³

Multiplicity of 4 diagram

(x+2)⁴

If a polynomial has a factor of (x-a)ⁿ and n is even, what does the graph look like?

Graph touches x-axis at x=a but doesn’t go under it

If a polynomial has a factor of (x-a)ⁿ and n is odd, what does the graph look like?

Graph crosses the x-axis

The arms of the graph will point … if the leading coefficient is positive

Up

The arms of the graph will point … if the leading coefficient is negative (Even)

Down

What is the leading coefficient of a polynomial?

The coefficient of the term with the highest power

If a polynomial is of odd degree then …

1 arm up and 1 arm down

The arms of the graph will point … if the leading coefficient is positive (Odd)

Right arm points up

The arms of the graph will point … if the leading coefficient is negative (Odd)

Right arm points down

When given the graph and after finding the factors, what should you do? (3)

Multiply out the roots. “a“ is placed on the outside to be multiplied in. Sub in a point and find what a is and sub it in.

When manipulating formulae how do you cancel a term that’s being multiplied?

Divide

When manipulating formulae how do you cancel a term that’s being divide?

Multiply

When manipulating formulae how do you cancel a term that’s being added?

Minus

When manipulating formulae how do you cancel a term that’s being minused?

Add

When manipulating formulae how do you handle a term with a square root?

Square

When manipulating formulae how do you cancel a term that’s being squared?

Square root