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.

Question

What is the vertex form of the graphed equation?

(1 point)
y=−2
y
=
−
2
(x−
x
−
)2+
2
+

Answer 1

To find the vertex form of a parabola that opens downward on a coordinate plane, we typically use the vertex form equation:

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

In this equation:

• \( (h, k) \) is the vertex of the parabola.
• \( a \) determines the direction and width of the parabola. Since the parabola opens downward, \( a \) will be a negative value.

From your question, it seems like part of the parameters are corrupted (like \( y = -2 \), \( x - \) portions, and the values).

To fill in the vertex form correctly, I need the x and y coordinates of the vertex \( (h, k) \) and the value of \( a \).

1. Identify the vertex: Look for the highest point on the graph as this will be your vertex \( (h, k) \).
2. Determine a: Decide how "wide" or "narrow" the parabola is based on the plotted point. If you provide or count another point on the parabola, we can find \( a \) using the vertex form equation.

For now, if you have \( h = 0 \) and \( k = -2 \) as an example vertex and \( a = -2 \) as a made-up value, the equation would look like this:

\[ y = -2(x - 0)^2 - 2 \]

Which simplifies to:

\[ y = -2x^2 - 2 \]

If you provide me with specific coordinates for the vertex and information about the downward opening of the parabola, I can give you the exact equation.