Monthly Archives: May 2018

Week 15- Adding and Subtracting Rational Expressions

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When adding or subtracting Rational Expressions, the denominator always has to be the same for all Expressions.

Step one: Make sure the denominator is the same by factoring both denominators and then multiplying the factors. If the two denominators have same factors, they cancel out. After you find the common denominator, you can combine the Fractions into one big fraction.

Step two: What you do to the bottom, you have to do to the top. We have to look at what could multiply 6x into 18xy, it would have to be 3y. So we multiply the numerator by 3y. Then we have to look at what multiplies 9y into 18xy, it would have to be 2x, so we multiply the numerator by 2x.

Step three: once the denominators are the same, and the numerator has been multiplied, we can combine the fractions into one big fraction, and simplify.

 

Week 13: Graphing Linead Reciprocal Functions

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This week I learned about graphing reciprocal functions.

Step 1: Graph the linear function:

Step 2: Identify the asymptotes by first identifying the invariant points (the invariant points are always at the 1 and -1 y-axis points on the linear function, the asymptote goes directly through the middle of the invariant points, the other asymptote is always on the x-axis).

Step 3: Graph the hyperbolas:

Week 12: Solving Quadratic Systems of Equations

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This week I learned about solving quadratic systems of equations.

A linear-quadratic system can have 3 possible solutions:

1) 2 solutions (line intersects parabola at 2 points)

2) 1 solution (Line intersects parabola at 1 point)

3) 0 solutions (line doesn’t intersect parabola)

A quadratic-quadratic system could have 4 possible solutions:

1) 2 solutions (parabolas intersect at 2 points)

2) 1 solution (parabolas intersect at 1 point)

3) 0 solutions (parabolas don’t intersect)

4) infinite solutions (parabolas are on top of one another)

How to solve a quadratic-quadratic system graphically:

Step one: Identify clues from the equations

Step two: graph the equations

Step three: Identify the intersects

The parabolas have 2 solutions (-2,-2) and (2,-2)

Week 11- Solving Quadratic Inequalities

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This week in math I learned about solving quadratic inequalities.

When solving quadratic inequalities, you always have to remember that if you are dividing by a negative, you have to flip the inequality sign.

Step 1: Find the roots of a quadratic inequality:

Step 2: Insert the roots into a numbe line:

Then you can pick 3 numbers from the 3 sections on the number line and insert them into the original equation.

I picked 0 becuase it is quick and easy:

I got a positive number so, any number below 2 is positive.

Then I did the same with the number 3:

I got a negative number, that means that all numbers between 2 and 7 would result in a negative number.

Then I did the same with 10 and got a positive number, which means all numbers above 7 would result in a positive number. But the equation is asking which number could be inserted into the equation that would result in negative number. Looking back at the number line I see that all numbers beteeen 2 and 7 would result in a negative number. So the answer is 2<x<7.