college math problem

Question

What is the vertex of f(x)=1/9x²

Also what is the equation of the axis of symmetry of f(x)=1/9x²

Evaluate f(-4)and f(5)

Answer 1

f(x)=(1/9)x²

 

for the parabola ax²+bx+c

we have a=1/9, b=0, c=0

 

The x coordinate of the vertex = -b/2a

= -0/(2/9) = 0

 

The y coordinate of the vertex is f(-b/2a) = f(0)

= (1/9)(0) = 0

 

the vertex is at the origin (0,0)

 

The axis of symmetry for a parabola with vertex (h,k) where the square term is the x variable is the line x=h

The axis of symmetry is x=0

 

f(-4)=(1/9)(-4)²= (1/9)(16) = 16/9

 

f(5)=(1/9)(5)²=(1/9)(25)=25/9