Ask a New Question
Menu

Use the image to answer the question.

A coordinate plane shows a parabola that opens downward with a plotted point. Both axes range from negative 8 to 8 in increments of 2.

What is the vertex form of the graphed equation?

(1 point)
y=−2
(x−
)2+
Skip to navigation

3 answers

To determine the vertex form of a parabola, which is given by the 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.

Since I cannot see the image you're referring to, I'll guide you through the steps to find the vertex form based on the information you could see in the graphed parabola:

  1. Identify the Vertex: Look for the point where the parabola reaches its maximum value (in a downward-opening parabola). This point is the vertex of the parabola, represented as \( (h, k) \).

  2. Determine the Value of \( a \): The coefficient \( a \) tells us how "narrow" or "wide" the parabola is. If you have another point on the graph (besides the vertex), use it to solve for \( a \) by substituting the coordinates of both the vertex and the additional point into the equation.

For example, if the vertex you found is \( (h, k) \) and you have another point \( (x_1, y_1) \):

\[ y_1 = a(x_1 - h)^2 + k \]

Rearranging this will help you solve for \( a \).

  1. Plug in the Values: Once you have \( a \), \( h \), and \( k \), you can write the equation in vertex form.

If you provide the specific coordinates of the vertex and any additional points, I can further assist you in writing the exact vertex form of the equation.

the coordinates are (-3, -1)

Given the vertex of the parabola is \((-3, -1)\), this means:

  • \( h = -3 \)
  • \( k = -1 \)

The vertex form of the parabola can be expressed as:

\[ y = a(x + 3)^2 - 1 \]

Next, to determine the value of \( a \), we need an additional point on the parabola. If you have a specific point \( (x_1, y_1) \) that lies on the parabola, we can substitute that into the equation to solve for \( a \).

For example, if you have another point, substitute its coordinates in:

\[ y_1 = a(x_1 + 3)^2 - 1 \]

Rearranging this will allow you to solve for \( a \).

If you do not have another point, we can write the vertex form as far as we can:

\[ y = a(x + 3)^2 - 1 \]

Please provide another point on the parabola if you have one to find the exact value of \( a \). Otherwise, the equation remains generalized until \( a \) is determined.