Find the Quadratic Equation: Converting Graph at Point (8,-2) to Algebraic Form

To solve for the algebraic representation of the parabola from the drawing:

• Step 1: Identify the vertex of the parabola. The drawing indicates the vertex at $(8, -2)$.
• Step 2: Write the vertex form of the parabola, $y = a(x - h)^2 + k$, using the vertex $(8, -2)$ as $h = 8$ and $k = -2$.
• Step 3: Determine the orientation of the parabola. The drawing suggests the parabola opens downward, indicating a negative value for $a$. Hence, $a < 0$.
• Step 4: Substitute the vertex and the orientation into the equation: $y = -1(x - 8)^2 - 2$, simplifying to $y = -(x - 8)^2 - 2$.

Therefore, the algebraic representation of the parabola is $y = -(x - 8)^2 - 2$.