Final answer:
The vertex of the graph of the given quadratic function can be found using the formula x = -b/2a and substituting the x-value back into the function to find the y-coordinate.
Step-by-step explanation:
The vertex of a function represents the highest or lowest point on the graph of the function. In this case, the vertex can be found using the formula: x = -b/2a, where a, b, and c are the coefficients of the quadratic function. Given the constant values a = 1, b = 10, and c = -200, we can calculate the x-coordinate of the vertex. Using x = -b/2a: x = -10/2(1) = -10/2 = -5. Therefore, the x-coordinate of the vertex is -5.
To find the y-coordinate of the vertex, substitute the x-coordinate back into the quadratic function: y = (1)(-5)^2 + 10(-5) - 200 = 25 - 50 - 200 = -225. Therefore, the y-coordinate of the vertex is -225.
Therefore, the vertex of the graph of the given function is (-5, -225).