Question
Which ordered pair is on the graph of y=x^2 + 2?
A. (5,49)
B. (4,10)
C. (-1,1)
D. (-6,38)
A. (5,49)
B. (4,10)
C. (-1,1)
D. (-6,38)
Answers
GPT-4o mini
To determine which ordered pair is on the graph of the equation \( y = x^2 + 2 \), we can substitute the \( x \)-value from each option into the equation and see if the resulting \( y \)-value matches the \( y \)-value from the ordered pair.
1. **Option A: (5, 49)**
\[
y = 5^2 + 2 = 25 + 2 = 27
\]
This does not match \( y = 49 \).
2. **Option B: (4, 10)**
\[
y = 4^2 + 2 = 16 + 2 = 18
\]
This does not match \( y = 10 \).
3. **Option C: (-1, 1)**
\[
y = (-1)^2 + 2 = 1 + 2 = 3
\]
This does not match \( y = 1 \).
4. **Option D: (-6, 38)**
\[
y = (-6)^2 + 2 = 36 + 2 = 38
\]
This matches \( y = 38 \).
From the evaluations above, the only ordered pair that lies on the graph of the equation \( y = x^2 + 2 \) is option **D: (-6, 38)**.
1. **Option A: (5, 49)**
\[
y = 5^2 + 2 = 25 + 2 = 27
\]
This does not match \( y = 49 \).
2. **Option B: (4, 10)**
\[
y = 4^2 + 2 = 16 + 2 = 18
\]
This does not match \( y = 10 \).
3. **Option C: (-1, 1)**
\[
y = (-1)^2 + 2 = 1 + 2 = 3
\]
This does not match \( y = 1 \).
4. **Option D: (-6, 38)**
\[
y = (-6)^2 + 2 = 36 + 2 = 38
\]
This matches \( y = 38 \).
From the evaluations above, the only ordered pair that lies on the graph of the equation \( y = x^2 + 2 \) is option **D: (-6, 38)**.