SOLUTION: Determine the maximum or minimum value of the function P(x)= -3x^2+6x+5 I have no idea where to even begin figuring out this problem. I know the answer is either 1 min,max or 8

Question 207627This question is from textbook
: Determine the maximum or minimum value of the function P(x)= -3x^2+6x+5
I have no idea where to even begin figuring out this problem. I know the answer is either 1 min,max or 8 min, max. Any help will be greatly appreciated. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The min/max is simply the y-coordinate of the vertex.

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 .

Divide.

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 min/max is the y-coordinate of the vertex, this means that the min/max is 8.

Now the question is: is this value a min or is it a max? Since the leading coefficient of is negative, this means that the value is a max. Graph the equation if you're not sure.

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