SOLUTION: What is the maximum value of the function f(x) = (3-x)(5x + 35)?

Question 149596: What is the maximum value of the function f(x) = (3-x)(5x + 35)?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, we need to find the zeros.

Set the expression equal to zero.

Now set each factor equal to zero:

or

Now solve for x for each factor:

or

So the zeros of are or

Now average the zeros to get

So the axis of symmetry (ie the x-coordinate of the vertex) is

Now plug in to find the y coordinate of the vertex

Start with the given function.

Plug in

Rewrite as

Multiply

Add

Multiply

So the y coordinate of the vertex is

This means that the vertex is at the point (-2,125). Since the vertex is either the highest or lowest point (in this case the highest), this means that that the maximum value of the function is
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