Honors Algebra II - Final Study Guide

short study guide of how to do things and some equations, etc.

Methods of Factoring

GCF, Trinomial Factoring, Perfect Square Trinomial, Grouping, Difference of Squares, AC Method or Guess and Check

Synthetic Division

Used to divide a binomial into a larger polynomial. Solve for the variable of the binomial (zero property), then use the coefficients of the greater polynomial to divide.

Simplification of Radicals

Remove all that you can from the radical and place it outside of the radical. Don’t forget i when dealing with negatives in even roots. In a polynomial, radicals behave as their own term.

Methods of Solving Quadratics

Factoring, Square Root Method, Completing the Square, Quadratic Formula

Square Root Method vs. Completing the Square

Square root method is the best option when presented with a perfect square binomial. You should move the constant on the other side of the equal sign, if necessary, then take the square root of both sides and solve from there. Completing the Square is a better option when presented with a prime trinomial with an even linear coefficient. Once again, move the constant to the other side if necessary. Then, divide the linear coefficient by two, and add the quotient to both sides. Factor the trinomial and then take the square root of both sides; you can solve from there.

Quadratic Formula

x=(-b±√b²-4ac)/2a

Multiplicities

Occur in a polynomial function when a zero is repeated two or more times and creates an irregularity on the graph. Written as (m#). Even multiplicity values cause the graph to bounce off the x-axis, while odd multiplicities cause the graph to create a cubic function shape when crossing the x axis.

End Behavior

The direction in which the arrows at the end of a polynomial function graph point. A positive leading coefficient yields down/up end behavior for an odd exponent and an up/up end behavior for an even exponent; however, a negative leading coefficient yields up/down end behavior for an odd exponent and a down/down end behavior for an even exponent.

Arithmetic with Radicals

Think of each radical as a variable; they function similarly. When adding and subtraction radicals, you cannot combine what is inside the radical unless you see like terms after you simplify. However, to multiply radicals you multiply the contents of both radicals into one single radical, then simply.

Extraneous Solution

A solution to an equation (for a variable) that can be found algebraically but doesn’t work in the actual function. For radical equations, an extraneous solution would cause there to be a negative number underneath a radical with an even root. For rational equations, an extraneous solution would cause there to be a zero in the denominator of the fraction.

Asymptote

Line in which the graph of a function will never cross; can be horizontal or vertical. They exist in exponential, logarithmic, and rational functions. You can have two vertical asymptotes in a rational function, if the denominator contains two factors. To show these, draw a dotted line where the asymptote should go and label it; if it is on an axis, extend the line a bit beyond the graph so you can see it is there. You can reflect points along an asymptote to help you graph functions too. These will be included in any domain restrictions as well.

Finding Intercepts

To find an x-intercept plug in 0 for y; to find a y-intercept plug in 0 for x. Write answers as points, if an intercept exists. Other tricks can also be used to find these values as well, depending on the function you’re dealing with (such as linear and quadratic functions).

Graphs & Sketches

Account for multiplicities and end behavior, and don’t forget to include x and y intercept, evening out the graph so it makes sense. Be familiar with quadratic, exponential, logarithmic and rational graphs.