Question

Which function has a vertex at the origin?
O f(x) = (x + 4)
O f(x) = x(x – 4)
O f(x) = (x – 4)(x + 4)
O f(x) = 2

Answer 1

Answer:

B) $f(x)=x(x-4)$

Step-by-step explanation:

To find the function which has vertex at the origin.

Solution:

For a function to have its vertex at origin the function must pass through point (0,0) which means $f(0)=0$.

We will find $f(0)$ for each of the given functions and check if it has vertex at origin.

To find $f(0)$ we will plugin $x=0$ in the function.

A) $f(x)=x+4$

$f(0)=0+4=4$

Vertex is  not at the origin.

B) $f(x)=x(x-4)$

$f(0)=0(0-4)=0$  [Any number times zero is = zero]

Vertex is at the origin.

C) $f(x)=(x-4)(x+4)$

$f(0)=(0-4)(0+4)=(-4)(4)=-16$

Vertex is  not at the origin.

D) $f(x)=2$

$f(0)=2$

Vertex is  not at the origin.