SOLUTION: I need to find the vertex for this problem f(x)= -3x^+x-5

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Question 164992: I need to find the vertex for this problem
f(x)= -3x^+x-5
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=-3x%5E2%2Bx-5, we can see that a=-3, b=1, and c=-5.


x=%28-%281%29%29%2F%282%28-3%29%29 Plug in a=-3 and b=1.


x=%28-1%29%2F%28-6%29 Multiply 2 and -3 to get -6.


x=1%2F6 Reduce.


So the x-coordinate of the vertex is x=1%2F6. Note: this means that the axis of symmetry is also x=1%2F6.


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


y=-3x%5E2%2Bx-5 Start with the given equation.


y=-3%281%2F6%29%5E2%2B1%2F6-5 Plug in x=1%2F6.


y=-3%281%2F36%29%2B1%2F6-5 Square 1%2F6 to get 1%2F36.


y=-1%2F12%2B1%2F6-5 Multiply -3 and 1%2F36 to get -1%2F12.


y=-59%2F12 Combine like terms.


So the y-coordinate of the vertex is y=-59%2F12.


So the vertex is .