https://file.aiquickdraw.com/mathbot/file/1727043653835ibqfskar.jpg

Yes, the equation provided in the image appears to be correct. Let's break it down:

The given quadratic equation is:

\[
g(x) = -2(x + 4)^2 + 5
\]

### Why this equation is correct:

1. **Vertex Form**: The equation is in vertex form:
   \[
   g(x) = a(x - h)^2 + k
   \]
   where \((h, k)\) is the vertex of the parabola, and \(a\) determines the direction and width of the parabola.

2. **Vertex**: From the graph, the vertex is at \((-4, 5)\). In the equation, \((h, k) = (-4, 5)\), which matches the graph. This means that \(h = -4\) and \(k = 5\), so the vertex form should indeed include \((x + 4)\) and the constant \(+5\).

3. **Direction and Shape**: The parabola opens downward, so \(a\) should be negative. The value \(a = -2\) causes the parabola to open downward and makes it "narrower" than the standard parabola.

4. **Points**: The graph also shows the point \((-6

Understand how to derive the quadratic equation g(x) = -2(x + 4)^2 + 5 from a graph of a parabola. This problem involves key concepts in quadratic functions, vertex form, and graphing. Suitable for students in Grades 8-10.

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