The quadratic function is .
Find the maximum or minimum values.
\The standard form of quadratic function , where
.
Rewrite the function .
and
.
Since , the function has a maximum value and opens down.
Maximum value of the function is coordinate of the vertex.
The coordinate of the vertex is
.
(Substitute the values
and
)
(Simplify)
The -coordinate of the vertex is
.
Find the -coordinate of the vertex by evaluating the function for
.
(Original function)
(Substitute
)
(Evaluate powers:
)
(Multiply)
(Substitute:
)
The maximum value of the function is .
Find domain and range of the function.
\The domain is all real numbers.
\The range is all real numbers less than or equal to maximum value or .
The function has maximum value.
\The maximum value of the function is .
Domain is all real numbers.
\The range is .