SOLUTION: y=x squared-12x+20 simplify into the parabala equasion

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Question 254966: y=x squared-12x+20
simplify into the parabala equasion
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You need to learn the language of math.
squared is ^2 ^ is over the 6
and spelling parabola not parabala
and equation not equasion

y=x^2-12x+20
y=x%5E2-12x%2B20
It already is a parabola equation.
Maybe you mean factor
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression x%5E2-12x%2B20, we can see that the first coefficient is 1, the second coefficient is -12, and the last term is 20.



Now multiply the first coefficient 1 by the last term 20 to get %281%29%2820%29=20.



Now the question is: what two whole numbers multiply to 20 (the previous product) and add to the second coefficient -12?



To find these two numbers, we need to list all of the factors of 20 (the previous product).



Factors of 20:

1,2,4,5,10,20

-1,-2,-4,-5,-10,-20



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to 20.

1*20 = 20
2*10 = 20
4*5 = 20
(-1)*(-20) = 20
(-2)*(-10) = 20
(-4)*(-5) = 20


Now let's add up each pair of factors to see if one pair adds to the middle coefficient -12:



First NumberSecond NumberSum
1201+20=21
2102+10=12
454+5=9
-1-20-1+(-20)=-21
-2-10-2+(-10)=-12
-4-5-4+(-5)=-9




From the table, we can see that the two numbers -2 and -10 add to -12 (the middle coefficient).



So the two numbers -2 and -10 both multiply to 20 and add to -12



Now replace the middle term -12x with -2x-10x. Remember, -2 and -10 add to -12. So this shows us that -2x-10x=-12x.



x%5E2%2Bhighlight%28-2x-10x%29%2B20 Replace the second term -12x with -2x-10x.



%28x%5E2-2x%29%2B%28-10x%2B20%29 Group the terms into two pairs.



x%28x-2%29%2B%28-10x%2B20%29 Factor out the GCF x from the first group.



x%28x-2%29-10%28x-2%29 Factor out 10 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



%28x-10%29%28x-2%29 Combine like terms. Or factor out the common term x-2



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Answer:



So x%5E2-12%2Ax%2B20 factors to %28x-10%29%28x-2%29.



In other words, x%5E2-12%2Ax%2B20=%28x-10%29%28x-2%29.



Note: you can check the answer by expanding %28x-10%29%28x-2%29 to get x%5E2-12%2Ax%2B20 or by graphing the original expression and the answer (the two graphs should be identical).