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Harman [31]
3 years ago
7

W(x) = x2 + 1; Find w(x + 3)

Mathematics
1 answer:
Tanzania [10]3 years ago
3 0

Given the function w:

\displaystyle \large{w(x) =  {x}^{2}  + 1  }

Since we want to find w(x+3), the input would be x+3.

Substitute x = x+3 in.

\displaystyle \large{w(x + 3) =  {(x + 3)}^{2}  + 1  }

<u>A</u><u>l</u><u>t</u><u>e</u><u>r</u><u>n</u><u>a</u><u>t</u><u>e</u><u> </u><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u>

The answer above works if you want it in vertex form. For this alternate solution, I will convert the function in standard form.

As we know:

\displaystyle \large{ {(x + y)}^{2}  =  {x}^{2}  + 2xy +  {y}^{2} }

Therefore:

\displaystyle \large{ {(x + 3)}^{2}  =  {x}^{2}  + 2(x)(3) +  {3}^{2} } \\  \displaystyle \large{ {(x + 3)}^{2}  =  {x}^{2}  + 6x+  9}

Now for function w:

\displaystyle \large{w(x + 3) =   {x}^{2}  + 6x + 9+ 1  } \\  \displaystyle \large{w(x + 3) =   {x}^{2}  + 6x + 10}

Hence:

  • The answer is w(x+3) = (x+3)^2+1 for vertex form
  • OR w(x+3) = x^2+6x+10
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