Question
what is the equation for a parabola with the points (-4,2)
Answers
GPT-4o mini
To find the equation of a parabola that passes through a specific point like \((-4, 2)\), we generally need more information (such as the vertex, another point, or the orientation of the parabola) because there are infinitely many parabolas that could go through any single point.
However, if we assume a simple form of a parabola, such as:
\[
y = ax^2 + bx + c
\]
We can plug in the known point to help determine the coefficients \(a\), \(b\), and \(c\). Let's say we assume the vertex of the parabola is at the origin (0,0) for simplicity. The equation then simplifies to:
\[
y = ax^2
\]
Plugging in the point \((-4, 2)\):
\[
2 = a(-4)^2
\]
\[
2 = 16a
\]
\[
a = \frac{2}{16} = \frac{1}{8}
\]
Thus, the equation of a parabola with a vertex at the origin and passing through the point \((-4, 2)\) is:
\[
y = \frac{1}{8}x^2
\]
If you have different specific requirements (like a different vertex or orientation), please provide that information, and I can help derive a corresponding equation!
However, if we assume a simple form of a parabola, such as:
\[
y = ax^2 + bx + c
\]
We can plug in the known point to help determine the coefficients \(a\), \(b\), and \(c\). Let's say we assume the vertex of the parabola is at the origin (0,0) for simplicity. The equation then simplifies to:
\[
y = ax^2
\]
Plugging in the point \((-4, 2)\):
\[
2 = a(-4)^2
\]
\[
2 = 16a
\]
\[
a = \frac{2}{16} = \frac{1}{8}
\]
Thus, the equation of a parabola with a vertex at the origin and passing through the point \((-4, 2)\) is:
\[
y = \frac{1}{8}x^2
\]
If you have different specific requirements (like a different vertex or orientation), please provide that information, and I can help derive a corresponding equation!