The vertex form of a quadratic function is expressed as
y = a(x - h)^2 + k
where
h and k are the x and y coordinates of the vertex
a is the leading coefficient(coefficient of the term with the highest exponent)
The standard form of a quadratic function is
f(x) = ax^2 + bx + c
The given function is
f(x)= x^2 - x
By comparing both functions,
a = 1
b = - 1
c = 0
We would calculate the coordinate of the vertex by using the formula
x = - b/2a
x = - - 1/2 * 1 = 1/2
We would find the y coordinate of the vertex by substituting x = 1/2 into the original function. We have
f(1/2) = (1/2)^2 - 1/2 = 1/4 - 1/2 = - 1/4
Thus,
h = 1/2
k = - 1/4
a = 1
The vertex is (1/2, - 1/4)
By substituting these values into the equation, the vertex form is
f(x) = (x - 1/2)^2 - 1/4