SOLUTION: I need help finding the vertex and determining the min or max of f(x) = -3x2 + 9x + 2

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Question 677751: I need help finding the vertex and determining the min or max of f(x) = -3x2 + 9x + 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%2B9x%2B2, we can see that a=-3, b=9, and c=2.


x=%28-%289%29%29%2F%282%28-3%29%29 Plug in a=-3 and b=9.


x=%28-9%29%2F%28-6%29 Multiply 2 and -3 to get -6.


x=3%2F2 Reduce.


So the x-coordinate of the vertex is x=3%2F2. Note: this means that the axis of symmetry is also x=3%2F2.


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=-3x%5E2%2B9x%2B2 Start with the given equation.


f%283%2F2%29=-3%283%2F2%29%5E2%2B9%283%2F2%29%2B2 Plug in x=3%2F2.


f%283%2F2%29=-3%289%2F4%29%2B9%283%2F2%29%2B2 Square 3%2F2 to get 9%2F4.


f%283%2F2%29=-27%2F4%2B9%283%2F2%29%2B2 Multiply -3 and 9%2F4 to get -27%2F4.


f%283%2F2%29=-27%2F4%2B27%2F2%2B2 Multiply 9 and 3%2F2 to get 27%2F2.


f%283%2F2%29=35%2F4 Combine like terms.


So the y-coordinate of the vertex is y=35%2F4.


So the vertex is .


Since the leading coefficient (which is -3) is negative, this means that the y coordinate of the vertex is the max of f(x).

So the max of f(x) is 35%2F4