Quadratic Equation: Finding Algebraic Form for Arc Through (-10,-3)

To determine the algebraic representation of the parabola, follow these steps:

• Step 1: Recognize the parabola vertex form, $y = (x - p)^2 + k$, which uses $(p, k)$ as the vertex.
• Step 2: Given that the vertex (from the drawing) is $(-10, -3)$, substitute these values into $p$ and $k$.
• Step 3: Utilizing vertex form, substitute $p = -10$ and $k = -3$ into the expression, resulting in: $y = (x + 10)^2 - 3$.

As a result, the parabola is represented algebraically by replacing $(x-p)^2$ with $(x - (-10))^2$, simplifying to $(x + 10)^2$, and adding $k$, i.e., $-3$.

Therefore, the equation that corresponds with the drawing is $y = (x + 10)^2 - 3$.