Answer:
[tex]f(x)=-x^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
where:
- (h, k) is the vertex
- a is some constant
If the vertex is at the origin, then (h, k) = (0, 0)
[tex]\implies f(x)=a(x-0)^2+0[/tex]
[tex]\implies f(x)=ax^2[/tex]
Comparing this with the answer options suggests that the function with a vertex at the origin is [tex]f(x)=-x^2[/tex]
