Asked by PJ
                You want to graph a parabola given by the equation  y=−14x2+x−4 . Which table of ordered pairs would match this parabola?
(1 point)
Responses
x y
2 -1
6 3
10 -1x y 2 -1 6 3 10 -1
x y
2 -3
0 -4
-2 -7x y 2 -3 0 -4 -2 -7
x y
2 -6
-6 -10
-10 -6x y 2 -6 -6 -10 -10 -6
x y
0 -1
-4 -5
-8 -1x y 0 -1 -4 -5 -8 -1
            
        (1 point)
Responses
x y
2 -1
6 3
10 -1x y 2 -1 6 3 10 -1
x y
2 -3
0 -4
-2 -7x y 2 -3 0 -4 -2 -7
x y
2 -6
-6 -10
-10 -6x y 2 -6 -6 -10 -10 -6
x y
0 -1
-4 -5
-8 -1x y 0 -1 -4 -5 -8 -1
Answers
                                                    There are no human answers yet.
                                            
                
                    Answered by
            GPT-4o mini
            
    To determine which table of ordered pairs corresponds to the parabola given by the equation \( y = -14x^2 + x - 4 \), we will evaluate the function at various \( x \) values and find the corresponding \( y \) values. 
Let's compute \( y \) for several \( x \) values:
1. **For \( x = 2 \):**
\[
y = -14(2^2) + (2) - 4 = -14(4) + 2 - 4 = -56 + 2 - 4 = -58
\]
2. **For \( x = 0 \):**
\[
y = -14(0^2) + 0 - 4 = -4
\]
3. **For \( x = -2 \):**
\[
y = -14(-2^2) + (-2) - 4 = -14(4) - 2 - 4 = -56 - 2 - 4 = -62
\]
4. **For \( x = -4 \):**
\[
y = -14(-4^2) + (-4) - 4 = -14(16) - 4 - 4 = -224 - 4 - 4 = -232
\]
Next, we can check against the provided pairs:
1. **First table:**
- \( (2, -1) \)
- \( (6, 3) \)
- \( (10, -1) \)
2. **Second table:**
- \( (2, -3) \)
- \( (0, -4) \)
- \( (-2, -7) \)
3. **Third table:**
- \( (2, -6) \)
- \( (-6, -10) \)
- \( (-10, -6) \)
4. **Fourth table:**
- \( (0, -1) \)
- \( (-4, -5) \)
- \( (-8, -1) \)
Comparing the computed values:
- For \( x = 2 \), we found \( y = -58 \), which does not match any pairs.
- For \( x = 0 \), we found \( y = -4 \), which matches the second table: \( (0, -4) \).
- For \( x = -2 \), we found \( y = -62 \), and for \( x = -4 \), we got \( y = -232 \), neither of which appear in the tables.
While none of the pairs match the computed points perfectly, the second table includes one known value.
Thus, the best match indicating one point is the **second table:**
\[
\begin{align*}
x & : y \\
2 & : -3 \\
0 & : -4 \\
-2 & : -7 \\
\end{align*}
\]
This is the closest option based on part of the results computed, even though it does not fully represent the parabola accurately for all mentioned values.
    
Let's compute \( y \) for several \( x \) values:
1. **For \( x = 2 \):**
\[
y = -14(2^2) + (2) - 4 = -14(4) + 2 - 4 = -56 + 2 - 4 = -58
\]
2. **For \( x = 0 \):**
\[
y = -14(0^2) + 0 - 4 = -4
\]
3. **For \( x = -2 \):**
\[
y = -14(-2^2) + (-2) - 4 = -14(4) - 2 - 4 = -56 - 2 - 4 = -62
\]
4. **For \( x = -4 \):**
\[
y = -14(-4^2) + (-4) - 4 = -14(16) - 4 - 4 = -224 - 4 - 4 = -232
\]
Next, we can check against the provided pairs:
1. **First table:**
- \( (2, -1) \)
- \( (6, 3) \)
- \( (10, -1) \)
2. **Second table:**
- \( (2, -3) \)
- \( (0, -4) \)
- \( (-2, -7) \)
3. **Third table:**
- \( (2, -6) \)
- \( (-6, -10) \)
- \( (-10, -6) \)
4. **Fourth table:**
- \( (0, -1) \)
- \( (-4, -5) \)
- \( (-8, -1) \)
Comparing the computed values:
- For \( x = 2 \), we found \( y = -58 \), which does not match any pairs.
- For \( x = 0 \), we found \( y = -4 \), which matches the second table: \( (0, -4) \).
- For \( x = -2 \), we found \( y = -62 \), and for \( x = -4 \), we got \( y = -232 \), neither of which appear in the tables.
While none of the pairs match the computed points perfectly, the second table includes one known value.
Thus, the best match indicating one point is the **second table:**
\[
\begin{align*}
x & : y \\
2 & : -3 \\
0 & : -4 \\
-2 & : -7 \\
\end{align*}
\]
This is the closest option based on part of the results computed, even though it does not fully represent the parabola accurately for all mentioned values.
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