Use the image to answer the question.

Question

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 5 to 10 in increments of 1. The y-axis ranges from negative 7 to 5 in increments of 1.

Use the graph to write the equation of the quadratic function in vertex form.

(1 point)
y=−12
(x−
)2+

Answer 1

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.

Given the description, we can find the vertex from the graph. Let's assume:

• The vertex \( (h, k) \) is at the point \((h, k)\) on the graph, where \(h\) is the x-coordinate of the vertex and \(k\) is the y-coordinate.

You mentioned that the equation starts with \(y = -12\), which is likely not the vertex value. Instead, you would need to find the correct \(a\), \(h\), and \(k\) values.

Here’s what you need to do to complete the equation:

1. Identify the vertex \((h, k)\) from the graph.
2. Determine the value of \(a\) (the coefficient that indicates the width and direction of the parabola).
3. Substitute the values into the vertex form.

Let's say you find the vertex to be at \((h, k)\) and after observation, \(a\) is determined to be \(-12\).

The complete equation would look like:

\[ y = -12(x - h)^2 + k \]

Please replace \(h\) and \(k\) with the appropriate values from the graph you have.