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Rewrite the function by completing the square F(x)=2x^2+13x+20

User Coolnodje
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2 Answers

2 votes

Answer:

the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help

User Tobse
by
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3 votes

Answer:


F(x)=2\left(x+(13)/(4)\right)^2-(9)/(8).

Explanation:

Consider the function
F(x)=2x^2+13x+20.

Rewrite it as follows:


F(x)=(2x^2+13x)+20=2\left(x^2+(13)/(2)x\right)+20=2\left(x^2+(13)/(2)x+\left((13)/(4)\right)^2-\left((13)/(4)\right)^2\right)+20=2\left(x^2+(13)/(2)x+(169)/(16)\right)-2\cdot (169)/(16)+20.

Since


x^2+(13)/(2)x+(169)/(16)=\left(x+(13)/(4)\right)^2,

you get


F(x)=2\left(x+(13)/(4)\right)^2+20-(169)/(8)=2\left(x+(13)/(4)\right)^2-(9)/(8).

User Sireesh Yarlagadda
by
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