Convert Quadratic Graph to Algebraic Equation: Finding Function with Point (5,0)

To solve this problem, we need to identify how the given parabola is translated from its standard form.

The standard form of a parabola is $y = x^2$. When a vertical translation occurs, the equation becomes $y = x^2 + c$, where $c$ shifts the parabola up or down along the y-axis.

In the graph, there is an indication that the minimum point (or vertex) of the parabola has been shifted upwards so that it crosses the $y$-axis at the point where $y = 5$. This tells us that the entire parabola has been shifted vertically upwards by 5 units. Therefore, $c = 5$.

Thus, the algebraic representation of the translated function is:

$y = x^2 + 5$

This matches exactly with choice 3 from the provided options.

Therefore, the solution to the problem is $y = x^2 + 5$.