What is the factored form for a Quadratic Function with it vertex at the origin?
To find the factored form of a quadratic function with the vertex at the origin, we first need to determine the equation of the quadratic function in vertex form. The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Since the vertex is at the origin (0, 0), we have:
f(x) = a(x - 0)^2 + 0
Simplifying further, we get:
f(x) = ax^2
Thus, the quadratic function with its vertex at the origin and in factored form is simply:
f(x) = ax^2