Answer: [tex]f(x)=-x^2[/tex]
Step-by-step explanation:
In mathematics,the starting point on a grid is called an origin. It is the point (0,0), where the x-axis and y-axis intercept.
Thus to check which function passing through the origin, we need to check for x=0, y=f(x) must equals to 0.
1. [tex]f(x)=(x+4)^2[/tex]
At x=0,[tex]f(0)=(0+4)^2=4^2=16[/tex]
⇒f(x) is not passing through origin.
2. [tex]f(x)=x(x-4)[/tex]
At x=0,[tex]f(0)=0(0-4)=0[/tex]
⇒f(x) passing through origin.
But the vertex form of equation is [tex]f(x)=x^2-4x-4+4=(x-2)^2-4[/tex]
⇒ vertex of f(x)=(2,4)
3. [tex]f(x)=(x-4)(x+4)[/tex]
At x=0,[tex]f(0)=(0-4)(0+4)=-4\times4=-16[/tex]
⇒f(x) is not passing through origin.
4. [tex]f(x)=-x^2[/tex]
At x=0,[tex]f(0)=0^2=0[/tex]
⇒f(x) passing through origin.
Vertex form of equation=[tex]f(x)=-1(x-0)+0[/tex]
⇒ vertex=(0,0)
Answer:
f(x) = –x2
Step-by-step explanation:
i just did the test and got it right
