SOLUTION: What is the optimal value of this function: y=-0.5x^2+2x+3

Question 253267: What is the optimal value of this function: y=-0.5x^2+2x+3
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Take note that is equivalent to since

To find the optimal value, we need to find 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 max/min occurs at the vertex as the 'y' value, this means that the max is . So the optimal value is is .

Here's a graph to visually confirm the answer:

Graph of with the vertex of (2,5). Here we can see that the largest y value is y=5.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
From dictionary.com:
op�ti�mal (ŏp'tə-məl)
adj. Most favorable or desirable; optimum
Sounds like a matter of opinion.
I like 377.
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If you're told in class that this is "wrong", object to it.

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