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Anna35 [415]
3 years ago
15

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

Mathematics
2 answers:
Ymorist [56]3 years ago
7 0

Answer:

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

k0ka [10]3 years ago
3 0

Answer:

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

Step-by-step explanation:

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

Rewrite it as follows:

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

Since

x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,

you get

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

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