Algebra 2 Final Exam

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A Quadratic Function(parabola)-

Polynomial Functions

A simpler process of dividing a polynomial by a binomial.

Sequences and Series

Let's say we have the problem (x-y)^5.

What we will do is look at what the exponent is and whatever the exponent is you'll find on the triangle. So in our equation the exponent is 5 so we'll go to line 5 on the triangle and start our equation by taking the first number in line 5, which is 1 and taking x and putting it to the 5th power. Then you'll add 5 because it's the next number in line 5, then put x to the 4th because you subtract 1 from the exponent as you move down. You'll also put y to the 1st because you add one as you move down. So then the next thing added is 10x^3y^2 because 10 is the next number in line 5, we subtracted 1 from the exponent before on x and we added one to the exponent before on y. If you keep doing this you should end up with 1x^5-5x^4y^1+10x^3y^2-10x^2y^3+5xy^4-1y^5. You also know it's subtraction then addition because in the original (x-y)^5 there's subtraction. Then you would just factor this problem down and you should end up with x^5-5x^4+10x^3-10x^2+5x-1.

Synthetic Division-

Has a greatest exponent of 2. They have a quadratic, linear, and constant term.

Infographic Credits

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References

Created By Sophia Thomas

"Patterns in Pascal's Triangle." Patterns in Pascal's Triangle. N.p., n.d. Web. 18 May 2016.

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Quadratic Functions

I'll walk you through steps in my own words on how to do synthetic division.

Step 1: First you'll take the part of your equation that is being divided and you'll equal it to zero and then solve that.

Step 2: Whatever number you get from step one you'll take that and put it in a box. Then beside it you will take coefficients in the other part of the equation and line them up. Then drop the first coefficient and multiply it and the number in the box. What you get is what you'll put under the second coefficient.

Step 3: Then you will add these two numbers together.

Step 4: Repeat steps 2 and 3 until you reach the last coefficient lined up.

Pascal's Triangle-

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To graph a quadratic function, let's say you have an equation of 3x^2-12x+6. You can take 5 numbers and plug into the equation where the x is. We can use 0, 1, 2, 3, 4. When we plug them into the equation we get 6, -3, -6, -3, 6; this is the y. So now you have the x and y coordinates and can graph them. That's all you have to do.

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