SOLUTION: f(x)=1/3x^2+2x+1 The vertex is?

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Question 486972: f(x)=1/3x^2+2x+1
The vertex is?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=%281%2F3%29x%5E2%2B2x%2B1, we can see that a=1%2F3, b=2, and c=1.


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


x=%28-2%29%2F%282%2F3%29 Multiply 2 and 1%2F3 to get 2%2F3.


x=-3 Divide.


So the x-coordinate of the vertex is x=-3. Note: this means that the axis of symmetry is also x=-3.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


f%28x%29=%281%2F3%29x%5E2%2B2x%2B1 Start with the given equation.


f%28-3%29=%281%2F3%29%28-3%29%5E2%2B2%28-3%29%2B1 Plug in x=-3.


f%28-3%29=%281%2F3%29%289%29%2B2%28-3%29%2B1 Square -3 to get 9.


f%28-3%29=3%2B2%28-3%29%2B1 Multiply 1%2F3 and 9 to get 3.


f%28-3%29=3-6%2B1 Multiply 2 and -3 to get -6.


f%28-3%29=-2 Combine like terms.


So the y-coordinate of the vertex is y=-2.


So the vertex is .