Question

Which function has a vertex at the origin?

Answer 1

Answer:

$f(x)=-x^2$

Step-by-step explanation:

Vertex form of a quadratic function:

$f(x)=a(x-h)^2+k$

where:

• (h, k) is the vertex
• a is some constant

If the vertex is at the origin, then (h, k) = (0, 0)

$\implies f(x)=a(x-0)^2+0$

$\implies f(x)=ax^2$

Comparing this with the answer options suggests that the function with a vertex at the origin is $f(x)=-x^2$