Question
Which of the fallowing is a point you can generate to create the parabola for the quadric equation y=-6x^2+3x+8
A. (-3,-55)
B. (-6,206)
C. (-3,323)
D. (-6,8)
A. (-3,-55)
B. (-6,206)
C. (-3,323)
D. (-6,8)
Answers
GPT-4o mini
To determine which point is on the parabola defined by the equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-values from the answer choices into the equation and see if the corresponding y-values match.
Let's evaluate each option:
1. **Option A: (-3, -55)**
\[
y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55
\]
This point is on the parabola.
2. **Option B: (-6, 206)**
\[
y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226
\]
This point is not on the parabola.
3. **Option C: (-3, 323)**
The calculation for \( (-3, -55) \) revealed that the corresponding y-value is \( -55 \). Therefore, \( (-3, 323) \) cannot be on the parabola as the y-coordinate does not match.
4. **Option D: (-6, 8)**
\[
y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226
\]
This point is also not on the parabola.
The only point from the options provided that lies on the parabola \( y = -6x^2 + 3x + 8 \) is **A. (-3, -55)**.
Let's evaluate each option:
1. **Option A: (-3, -55)**
\[
y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55
\]
This point is on the parabola.
2. **Option B: (-6, 206)**
\[
y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226
\]
This point is not on the parabola.
3. **Option C: (-3, 323)**
The calculation for \( (-3, -55) \) revealed that the corresponding y-value is \( -55 \). Therefore, \( (-3, 323) \) cannot be on the parabola as the y-coordinate does not match.
4. **Option D: (-6, 8)**
\[
y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226
\]
This point is also not on the parabola.
The only point from the options provided that lies on the parabola \( y = -6x^2 + 3x + 8 \) is **A. (-3, -55)**.