Question
Use the graph to write the equation of the quadratic function in vertex form. (1 point)
image shows a curved line looking downwards. located at 3, 2
image shows a curved line looking downwards. located at 3, 2
Answers
Answered by
GPT-4o mini
To write the equation of a quadratic function in vertex form, you can use the following formula:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the direction and width of the parabola.
Based on your description, the vertex is at the point \((3, 2)\). Therefore, \(h = 3\) and \(k = 2\). The equation in vertex form thus starts as:
\[
y = a(x - 3)^2 + 2
\]
To find the value of \(a\), you would typically need a second point on the graph. If we assume a point is given (or if you have one from the image), plug in the \(x\) and \(y\) coordinates of that point to solve for \(a\).
For example, let's say there is another point \((x_1, y_1)\) on the graph. You would substitute \(x_1\) and \(y_1\) into the equation, and then solve for \(a\).
If you provide the coordinates of a second point, I can help you find \(a\) and complete the equation. If there is no second point provided, and the parabola opens downwards, you can choose a reasonable value for \(a\) (like -1). For example, if \(a = -1\), the equation would be:
\[
y = -(x - 3)^2 + 2
\]
Please provide additional information, and I can assist further!
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the direction and width of the parabola.
Based on your description, the vertex is at the point \((3, 2)\). Therefore, \(h = 3\) and \(k = 2\). The equation in vertex form thus starts as:
\[
y = a(x - 3)^2 + 2
\]
To find the value of \(a\), you would typically need a second point on the graph. If we assume a point is given (or if you have one from the image), plug in the \(x\) and \(y\) coordinates of that point to solve for \(a\).
For example, let's say there is another point \((x_1, y_1)\) on the graph. You would substitute \(x_1\) and \(y_1\) into the equation, and then solve for \(a\).
If you provide the coordinates of a second point, I can help you find \(a\) and complete the equation. If there is no second point provided, and the parabola opens downwards, you can choose a reasonable value for \(a\) (like -1). For example, if \(a = -1\), the equation would be:
\[
y = -(x - 3)^2 + 2
\]
Please provide additional information, and I can assist further!