To rewrite the quadratic function f(x) = 2x^2 - 10x in vertex form, we need to complete the square. The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the vertex.
Let's complete the square:
f(x) = 2x^2 - 10x
= 2(x^2 - 5x)
To complete the square, we need to take half of the coefficient of the x-term (-5), square it, and add it inside the parentheses:
f(x) = 2(x^2 - 5x + (-5/2)^2) - 2(-5/2)^2
= 2(x^2 - 5x + 25/4) - 2(25/4)
= 2(x^2 - 5x + 25/4) - 25/2
Now we can rewrite the function in vertex form:
f(x) = 2(x - 5/2)^2 - 25/2
The vertex of the quadratic function is given by the coordinates (h, k), where h = 5/2 and k = -25/2. Therefore, the vertex of the function f(x) = 2x^2 - 10x is V(5/2, -25/2).