Question

Which function has a vertex at the origin?

O f(x) = (x+4)²
Of(x) = x(x-4)
Of(x)=(x-4)(x + 4)
Of(x) = -x²

Answer 1

(d) f(x) = -x²

Explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

f(x) = -x² . . . . . a=-1