To determine the vertex form of the equation of the parabola, we need to identify the vertex coordinates.
Given the plotted point (-3, -1), we can assume that this is the vertex of the parabola, based on the information provided. The vertex form of a parabola is represented as:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. In your case, since the vertex is at (-3, -1):
- \(h = -3\)
- \(k = -1\)
Now, the only thing we need to find is the value of \(a\). We see that the parabola opens downward, which indicates that \(a\) will be negative.
Let's assume \(a = -2\) as indicated by your question, making our equation look like this:
\[ y = -2(x + 3)^2 - 1 \]
Thus, the completed form is:
\[ y = -2(x - (-3))^2 + (-1) \]
So, filling the blanks in the form \(y = −2(x−_)^2 + _\):
- \( _ = -3 \)
- \( _ = -1 \)
In summary, the vertex form of the graphed equation is:
\[ y = -2(x + 3)^2 - 1 \]
And the values for the blanks would be:
(-3, -1) in the vertex form answer.