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Greeley [361]
3 years ago
14

Rewrite the function by completing the square. f(x)=x^{2}+8x+4

Mathematics
1 answer:
xxMikexx [17]3 years ago
4 0

Answer:

\implies f(x) = ( x + 2)^2

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

  • f(x) = x² + 8x + 4 .

And we need to rewrite the function by completing the square. The function is ,

\implies f(x) = x^2+8x + 4

  • We can rewrite the function in the form of ,

\implies ( a + b)^2= a^2+b^2+2ab

<u>Rewriting</u><u> the</u><u> </u><u>function</u><u> </u><u>:</u><u>-</u><u> </u>

\implies f(x) = x^2+8x + 4\\\\\implies f(x) = x^2 + 2.2.2x + 2^2

  • This is similar to the whole square form stated above . So ,

\implies f(x) = ( x + 2)^2

<u>Hence </u><u>the </u><u>function</u><u> </u><u>in </u><u>whole</u><u> square</u><u> </u><u>form </u><u>is </u><u>(</u><u>x </u><u>+</u><u> </u><u>2</u><u>)</u><u>²</u><u> </u><u>.</u>

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\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}

Step-by-step explanation:

Use formulas for the volumes:

V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.

1. When r=1,

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V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.

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V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.

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\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.

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