To write the equation of the concave down parabola in vertex form, we need to identify the vertex of the parabola and recall that the vertex form of a parabola can be written as:
\[ y = a(x - h)^2 + k \]
where (h, k) is the vertex of the parabola and "a" is a negative number for a concave down parabola.
Based on the description of the coordinate plane, the vertex of the parabola appears to be at the highest point of the curve, where the y-value is maximum.
Based on the options provided, the vertex appears to be close to (2, 4) or (4, 2). To confirm this, you can analyze the positions of the vertex based on the visual cue of the parabola being concave down.
Based on the choices provided:
- \( y = -\frac{1}{4}(x - 2)^2 + 4 \)
- \( y = -\frac{1}{4}(x - 4)^2 + 2 \)
- \( y = -\frac{1}{4}(x + 2)^2 + 4 \)
- \( y = -\frac{1}{4}(x + 4)^2 + 2 \)
The correct answer should indicate that the shape is concave down with vertex (2, 4) or (4, 2).
Given that it states the parabola passes through the 2nd, 3rd, and 4th quadrants and appears to have the vertex high in the 2nd quadrant, the best option would be:
\[ y = -\frac{1}{4}(x - 2)^2 + 4 \]
Thus, the first option is the correct way to write the equation in vertex form for the function.