Question
In vertex form, write the equation for the quadratic function shown on the graph.
(3, 1)
(1 point)
y=3
𝑦
=
3
(x−
𝑥
−
)2+
2
+
(3, 1)
(1 point)
y=3
𝑦
=
3
(x−
𝑥
−
)2+
2
+
Answers
GPT-4o mini
To write the equation of a quadratic function in vertex form, we use the formula:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola and \(a\) is a coefficient that affects the width and direction of the parabola.
From the information provided, we have a point (3, 1). For a complete vertex form equation, we also need the vertex. However, since the options seem incomplete (it stops with "+") and don’t provide a vertex, let’s assume that the vertex of the quadratic function is (h, k), and that point (3, 1) is either the vertex or another point on the parabola if we had the vertex given.
Assuming the vertex is at (h, k) = (3, 1) and \(a = 1\) (which means the parabola opens upwards with a standard shape), the vertex form would be:
\[
y = a(x - 3)^2 + 1
\]
If we want to maintain the structure provided in your original text with a coefficient of \(3\):
\[
y = 3(x - 3)^2 + 1
\]
However, if you have different vertex values or if you know a specific value for \(a\) (not as an assumption), please provide that to accurately rewrite the equation.
Ultimately, the full equation will depend on additional information to clarify \(h\), \(k\), and \(a\).
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola and \(a\) is a coefficient that affects the width and direction of the parabola.
From the information provided, we have a point (3, 1). For a complete vertex form equation, we also need the vertex. However, since the options seem incomplete (it stops with "+") and don’t provide a vertex, let’s assume that the vertex of the quadratic function is (h, k), and that point (3, 1) is either the vertex or another point on the parabola if we had the vertex given.
Assuming the vertex is at (h, k) = (3, 1) and \(a = 1\) (which means the parabola opens upwards with a standard shape), the vertex form would be:
\[
y = a(x - 3)^2 + 1
\]
If we want to maintain the structure provided in your original text with a coefficient of \(3\):
\[
y = 3(x - 3)^2 + 1
\]
However, if you have different vertex values or if you know a specific value for \(a\) (not as an assumption), please provide that to accurately rewrite the equation.
Ultimately, the full equation will depend on additional information to clarify \(h\), \(k\), and \(a\).