SOLUTION: find the vertex of the parobola f(x)=-4x^2+40x-93

Question 109691: find the vertex of the parobola f(x)=-4x^2+40x-93
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the vertex, we need to know the axis of symmetry

To find the axis of symmetry, use this formula:

From the equation we can see that a=-4 and b=40

Plug in b=40 and a=-4

Multiply 2 and -4 to get -8

Reduce

So the axis of symmetry is

So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given polynomial

Plug in

Raise 5 to the second power to get 25

Multiply 4 by 25 to get 100

Multiply 40 by 5 to get 200

Now combine like terms

So the vertex is (5,7)

Notice if we graph the equation we get

and we can see that the vertex is (5,7)

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