Question

Use the table to answer the question.

x y
4 ?
6 ?
8 ?
12 ?
The table represents the equation y=2x−8−−−−−√−3
. Find the missing values to three decimal places in the table to produce the graph of the function.

(1 point)
Responses

−3
, −1
, −0.172
, 0.162
negative 3, negative 1, negative 0 point 1 7 2, 0.162 - no response given

−3
, −1
, −0.172
, 1
negative 3, negative 1, negative 0 point 1 7 2, 1 - no response given

−3
, −1.586
, −1
, −0.551
negative 3, negative 1 point 5 8 6, negative 1, negative 0 point 5 5 1 - incorrect

1, 1.732, 2.236, 3.606

Answer 1

To find the missing values for \( y \) given the equation \( y = \sqrt{2x - 8} - 3 \), we can substitute the values of \( x \) from the table into the equation.

1. For \( x = 4 \):
\[
y = \sqrt{2(4) - 8} - 3 = \sqrt{8 - 8} - 3 = \sqrt{0} - 3 = 0 - 3 = -3
\]

2. For \( x = 6 \):
\[
y = \sqrt{2(6) - 8} - 3 = \sqrt{12 - 8} - 3 = \sqrt{4} - 3 = 2 - 3 = -1
\]

3. For \( x = 8 \):
\[
y = \sqrt{2(8) - 8} - 3 = \sqrt{16 - 8} - 3 = \sqrt{8} - 3 \approx 2.828 - 3 \approx -0.172 \text{ (to three decimal places)}
\]

4. For \( x = 12 \):
\[
y = \sqrt{2(12) - 8} - 3 = \sqrt{24 - 8} - 3 = \sqrt{16} - 3 = 4 - 3 = 1
\]

Thus, the completed table with the values of \( y \) is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
4 & -3 \\
6 & -1 \\
8 & -0.172 \\
12 & 1 \\
\hline
\end{array}
\]

So the values are:
- For \( x = 4 \), \( y = -3 \)
- For \( x = 6 \), \( y = -1 \)
- For \( x = 8 \), \( y = -0.172 \)
- For \( x = 12 \), \( y = 1 \)

The correct response with three decimal places is:
\[
-3, -1, -0.172, 1
\]