SOLUTION: Without graphing, find the vertex and the maximum and minimum value of f(x) f(x)= -4/7(x-4)^2+8

Question 753632: Without graphing, find the vertex and the maximum and minimum value of f(x)
f(x)= -4/7(x-4)^2+8
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
is a quadratic function, so its graph is a parabola.
is the equation of that parabola in vertex form.
The vertex form is the form that makes it easiest to find the vertex.
When and
For all other values of ,
, , and
No matter what value takes,
and only when .
The function has a maximum at ,
and the value of that maximum is .
That corresponds to the vertex of the parabola, the point (4,8).
The function does not have a minimum; it can take any negative value you can think of.
The graph looks like this:

Parabolas can look like this or like this
They can have a maximum or a minimum, but not both, and whichever they have happens at the vertex.
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