SOLUTION: Parabolas Determine the vertex of the given equation. y = 3x2 - 3x + 2

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Question 453211: Parabolas
Determine the vertex of the given equation.
y = 3x2 - 3x + 2
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%5E2-3x%2B2, we can see that a=3, b=-3, and c=2.


x=%28-%28-3%29%29%2F%282%283%29%29 Plug in a=3 and b=-3.


x=%283%29%2F%282%283%29%29 Negate -3 to get 3.


x=%283%29%2F%286%29 Multiply 2 and 3 to get 6.


x=1%2F2 Reduce.


So the x-coordinate of the vertex is x=1%2F2. Note: this means that the axis of symmetry is also x=1%2F2.


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


y=3x%5E2-3x%2B2 Start with the given equation.


y=3%281%2F2%29%5E2-3%281%2F2%29%2B2 Plug in x=1%2F2.


y=3%281%2F4%29-3%281%2F2%29%2B2 Square 1%2F2 to get 1%2F4.


y=3%2F4-3%281%2F2%29%2B2 Multiply 3 and 1%2F4 to get 3%2F4.


y=3%2F4-3%2F2%2B2 Multiply -3 and 1%2F2 to get -3%2F2.


y=5%2F4 Combine like terms.


So the y-coordinate of the vertex is y=5%2F4.


So the vertex is .