SOLUTION: Find the vertex and the equation of the line of symmetry for {{{f(x)=(1/3)x^2}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex and the equation of the line of symmetry for {{{f(x)=(1/3)x^2}}}      Log On


   

Question 130761: Find the vertex and the equation of the line of symmetry for f%28x%29=%281%2F3%29x%5E2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%281%2F3%29x%5E2 Start with the given equation


f%28x%29=%281%2F3%29x%5E2%2B0x Add 0x to the equation. Note: this does not change the equation


From the equation f%28x%29=%281%2F3%29x%5E2%2B0x we can see that a=1%2F3 and b=0

x=%28-0%29%2F%282%2A%281%2F3%29%29 Plug in a=1%2F3 and b=0


x=0%2F%282%2F3%29 Simplify


x=0 Divide


So the x-coordinate of the vertex is x=0. This means that the equation of the line of symmetry is x=0




Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%280%29


f%28x%29=%281%2F3%29x%5E2 Start with the given equation


f%280%29=%281%2F3%29%2A0%5E2Plug in x=0


f%280%29=%281%2F3%29%2A0 Raise 0 to the second power to get 0


f%280%29=0 Multiply 1%2F3 and 0 to get 0



So the y-coordinate of the vertex is y=0


So the vertex is (0,0)



If we graph the equation, we can visually verify our answer.

Graph of f%28x%29=%281%2F3%29x%5E2 with a vertex of (0,0) and the line of symmetry of x=0 (blue line)