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The quadratic functions 
f(x) and 
g(x) are described in the table.





x

f(x)

g(x)


-6
36
4


-5
25
1


-4
16
0


-3
9
1


-2
4
4


-1
1
9


0
0
16


1
1
25


2
4
36




In which direction and by how many units should 
f(x) be shifted to match 
g(x) ?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units

Search res\newlineFacebook\newlinedodge car\newlineDieHard P\newlinecar batter\newline(15681568) Tain\newlineCopy of 88\newlineScienti:\newlineFLVS\newlineB Lessons\newlineAssessments\newlineGradebook\newlineEmail 11\newlineTools\newlineThe quadratic functions f(x) \mathrm{f}(\mathrm{x}) and g(x) \mathrm{g}(\mathrm{x}) are described in the table.\newline\begin{tabular}{|c|c|c|}\newline\hlinex x & f(x) f(x) & g(x) g(x) \\\newline\hline6-6 & 3636 & 44 \\\newline\hline5-5 & 2525 & 11 \\\newline\hline4-4 & 1616 & 00 \\\newline\hline3-3 & 99 & 11 \\\newline\hline2-2 & 44 & 44 \\\newline\hline1-1 & 11 & 99 \\\newline\hline 00 & 00 & 1616 \\\newline\hline 11 & 11 & 2525 \\\newline\hline 22 & 44 & 3636 \\\newline\hline\newline\end{tabular}\newlineIn which direction and by how many units should f(x) f(x) be shifted to match g(x) g(x) ?\newlineLeft by 44 units\newlineRight by 44 units\newlineLeft by 88 units\newlineRight by 88 units

Full solution

Q. Search res\newlineFacebook\newlinedodge car\newlineDieHard P\newlinecar batter\newline(15681568) Tain\newlineCopy of 88\newlineScienti:\newlineFLVS\newlineB Lessons\newlineAssessments\newlineGradebook\newlineEmail 11\newlineTools\newlineThe quadratic functions f(x) \mathrm{f}(\mathrm{x}) and g(x) \mathrm{g}(\mathrm{x}) are described in the table.\newline\begin{tabular}{|c|c|c|}\newline\hlinex x & f(x) f(x) & g(x) g(x) \\\newline\hline6-6 & 3636 & 44 \\\newline\hline5-5 & 2525 & 11 \\\newline\hline4-4 & 1616 & 00 \\\newline\hline3-3 & 99 & 11 \\\newline\hline2-2 & 44 & 44 \\\newline\hline1-1 & 11 & 99 \\\newline\hline 00 & 00 & 1616 \\\newline\hline 11 & 11 & 2525 \\\newline\hline 22 & 44 & 3636 \\\newline\hline\newline\end{tabular}\newlineIn which direction and by how many units should f(x) f(x) be shifted to match g(x) g(x) ?\newlineLeft by 44 units\newlineRight by 44 units\newlineLeft by 88 units\newlineRight by 88 units
  1. Identify common y-values: Look at the x-values where f(x)f(x) and g(x)g(x) have the same y-values. For f(x)f(x), the y-value is 00 at x=0x=0. For g(x)g(x), the y-value is 00 at x=4x=-4.
  2. Shift f(x)f(x) left: Since the zeros of the functions are 44 units apart, with g(x)g(x) having a zero at a smaller xx-value, f(x)f(x) needs to be shifted to the left to match g(x)g(x).
  3. Calculate shift distance: The shift is exactly 44 units to the left because that's the difference between the xx-values of the zeros of f(x)f(x) and g(x)g(x).

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