Question
What is the vertex form of the equation in the graph?
(-2, -8)
(1 point)
y=
𝑦
=
(x−
𝑥
−
)2+
2
+
(-2, -8)
(1 point)
y=
𝑦
=
(x−
𝑥
−
)2+
2
+
Answers
GPT-4o mini
To write the vertex form of a quadratic equation given a vertex, we use the formula:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
You mentioned the vertex at \((-2, -8)\). Thus, \(h = -2\) and \(k = -8\). Plugging in these values into the vertex form gives:
\[
y = a(x + 2)^2 - 8
\]
Now, we need to determine the value of \(a\). The value of \(a\) affects the width and direction of the parabola (whether it opens upwards or downwards).
If you have an additional point on the graph, we can substitute the x-value of that point into the equation along with the corresponding y-value to solve for \(a\). If you don't have another point, \(a\) can remain as a variable.
Thus, the vertex form with the given vertex is:
\[
y = a(x + 2)^2 - 8
\]
If you want to specify a value for \(a\) or have more information about the parabola, please provide that info!
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
You mentioned the vertex at \((-2, -8)\). Thus, \(h = -2\) and \(k = -8\). Plugging in these values into the vertex form gives:
\[
y = a(x + 2)^2 - 8
\]
Now, we need to determine the value of \(a\). The value of \(a\) affects the width and direction of the parabola (whether it opens upwards or downwards).
If you have an additional point on the graph, we can substitute the x-value of that point into the equation along with the corresponding y-value to solve for \(a\). If you don't have another point, \(a\) can remain as a variable.
Thus, the vertex form with the given vertex is:
\[
y = a(x + 2)^2 - 8
\]
If you want to specify a value for \(a\) or have more information about the parabola, please provide that info!