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C(x)=x^2+6x+14 find vertex form

User Persia
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1 Answer

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Answer:

c(x)=(x+3)^2+5

Explanation:

To complete the square, the same value needs to be added to both sides.

So, to complete the square x^2+6x+9=(x+3)^2 add 9 to the expression

C(x) =x^2 +6x + 9 + 14

Since 9 was added to the right-hand side also add 9 to the left-hand side

C(x) +9= x^2 +6x + 9 + 14

Using a^2 + 2ab + b^2=(a+b)^2, factor the expression

C(x)+9= (x+3)^2 +14

Move constant to the right-hand side and change its sign

C(x)=(x+3)^2 +14 - 9

Subtract the numbers

C(x)= (x+3)^2 +5

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