Sample Review Problems for Quad Formula and Imaginary Numbers

If you missed class today (Mon Dec. 16th) please check the video links below on how to solve problems with the quadratic formula and how to simplify expressions with imaginary numbers.

How to Solve with Quadratic Formula:


How to Simplify with Imaginary Numbers:

Review Week for the Semester Exam (12/12 Through 12/18)

Hello algebra two students! We are done learning new material for the nine weeks and have entered the review period. Semester exams are the 19th and 20th. Here is our review schedule:

Thurs 12/12: Graphing review (parabolas, piecewise, inequalities, 3-d coordinate plane)
Fri 12/13: Matrices review (determinants, inverses, identities, solving for variables)
Mon: 12/16: Quadratic formula and imaginary numbers
Tues 12/17: Factoring (GCF, trinomials, dividing trinomials)
Wed 12/18: Exponent Rules, semester wrap-up

If you need help AT ALL please come and see me during a time that we are both free. I am more than happy to help you out, just communicate to me that you need it. Review sheets are going to be due on Wednesday. I will release some practice problems on Wednesday to help you study more. Good luck and happy studying!

Negative Rational Exponents and Solving Rational Equations

Negative rational (fraction) exponents are just like regular negative exponents. To get rid of a negative exponent, we put it on the other side of the fraction bar. Likewise, whenever we see a negative fraction exponent, move it (and the base number) to the other side of the fraction bar to make it positive, then solve as usual. Easy!

To see an example of this, click below:

Rational Equations are equations with powers in them. For example, we could see something like x^5 = 243. To solve these types of equations, we need to think OPPOSITES:

x^2 is the opposite of radical 2.
x^3 is the opposite of radical 3.
x^4 is the opposite of radical 4.
x^5 is the opposite of radical 5.....and so on. Do the opposite to each side until you get x by itself.

To see an example of how to solve a rational equation, click below:

Rational exponents

Rational exponents are exponents that are fractions. We re-write them so that the top number is an exponent and the bottom number is a radical. Then, we simplify both the exponent and the radical to get our answer. Note that order doesn't matter - you can do either the exponent or the radical first and you will get the same answer.

For a video example on how to do this, click here:
http://www.educreations.com/lesson/view/rational-exponents/14387309/?s=CO1gBl&ref=app

Multiplying Polynomials

A polynomial is a term that has at least one variable, a plus or minus sign, and at least two terms.  When multiplying Polynomials, we need to remember the exponent rules for multiplication: multiply the base and add the exponent. Distribute your terms to everything on the inside of the parentheses.  For two full length examples on how to do this, please click the links below. One is an example of multiplying polynomials and the other is what to do if you a polynomial expression to the third power. Enjoy!

http://www.educreations.com/lesson/view/multiplying-polynomials/13770520/?s=rq90dK&ref=app

http://www.educreations.com/lesson/view/binomial-cube/13770838/?s=zVmwt3&ref=app

Exponent Rules

Today we discussed the three exponent rules that everyone should know: the multiplication rule, the power rule, and the division rule.  When multiplying with exponents, we multiply the bases (big numbers) and add the exponents of like terms. When multiplying with exponents on the outside of parentheses, put your bases to the power of the outside exponent and multiply your exponents inside with the one outside. When dividing with exponents, divide the bases and subtract the exponents.

Note: if you get a negative exponent when dividing, change it to a positive exponent by putting it in the denominator.

To see video examples on how to use these three rules, click here:

http://www.educreations.com/lesson/view/multiplication-rule/13607398/?s=v2LhdR&ref=app
Multiplication Rule

http://www.educreations.com/lesson/view/power-rule/13607503/?s=KnSbkN&ref=app
Power rule

http://www.educreations.com/lesson/view/division-rule/13607615/?s=RBSuTS&ref=app
Division Rule

Simplifying with Imaginary Numbers

Imaginary numbers are slightly different than other variables. We know that i is the same thing as the square root of -1, which doesn't make any sense, so we leave it in the problem. But what if we see i to the second power? We plug in a -1 instead! Why is this important? Because we cannot have anything higher than i in the solution to a problem. Therefore, if we see i squared in a problem, we must change it to -1 instead and then simplify.

To see a few examples on how to simplify expressions with i in them, please click the link below:

http://www.educreations.com/lesson/view/simplifying-radicals/13379407/?s=5goBUq&ref=app