Use the image to answer the question.

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+
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Answer 1

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 $a$.

3. 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.

Answer 2

the coordinates are (-3, -1)

Answer 3

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.