Find the Algebraic Equation: Quadratic Function with Radius 6

Find the corresponding algebraic representation for the function

To solve this problem, we need to identify the algebraic representation of the given graph of a function. Based on the observation of the parabola, which opens downward and intersects the y-axis at the point $y = 6$, we can deduce its form.

Step 1: Identify the type of parabola.
The graph shows a parabola opening downwards, indicating that the leading coefficient $a$ in the equation $y = ax^2 + c$ is negative.

Step 2: Identify key points on the graph.
Since the parabola intersects the y-axis at $y = 6$, this means when $x = 0$, $y = 6$. Thus, the equation $y = ax^2 + c$ simplifies to $y = -x^2 + 6$.

Step 3: Confirmation of the algebraic representation.
From the downward orientation and the vertical intersection at $y = 6$ without any lateral shifts, the equation $y = -x^2 + 6$ fully describes the parabola.

Therefore, the corresponding algebraic representation of the function is $y = -x^2 + 6$.