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

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) (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: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Reduce.

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

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

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

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
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