Quadratic Equation: Finding Algebraic Expression for Point (5,-4)

To solve this problem, we'll use the vertex form of a parabola equation, $y = (x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola.

Step 1: We have the point $(5, -4)$ that indicates the vertex of the parabola.

Step 2: Substitute $h = 5$ and $k = -4$ into the vertex form equation.

By substitution, the equation becomes:

$y = (x - 5)^2 - 4$

Therefore, the algebraic representation of the parabola is $\mathbf{y = (x - 5)^2 - 4}$.