The function that has vertex at the origin is f(x) = –x², the correct option is D.
What is a Function?
A function is a law that relates two variables, a dependent and an independent variable with each other.
The domain and range of a function is always defined, the domain is all the values that can be an input to the function and the range is all the valuess that a function can have.
The functions are
f(x) = (x + 4)²
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x²
The general formula of a parabolic equation is
y = a(x-h)² +k, here (h,k) is the vertex of the parabola.
The functions 1 is f(x) = (x + 4)²
The value of h = -4, so the vertex is not at origin.
The function 2 is f(x) = x(x – 4)
f(x) has to be written in the standard form like,
f(x) = (x - 2)² -4
It has the vertex at (2, -4)
The function 3 is f(x) = (x – 4)(x + 4)
f(x) has to be written in the standard form like,
f(x) = x² -16
It has the vertex at ( 0 , -16)
The function 4 is, f(x) = –x²
The value of h and k is ( 0, 0)
The function has the vertex at origin.
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