$\"\"$

\

The quadratic function is $\"\"$ .

\

Find the maximum or minimum values.

\

The standard form of quadratic function $\"\"$ , where $\"\"$ .

\

Rewrite the function is $\"\"$ .

\

$\"\"$ and $\"\"$ .

\

\

Since $\"\"$ , the function has a minimum value and open up.

\

\

The equation of the axis symmetry is $\"\"$ .

\

$\"\"$ (Substitute the values $\"\"$ and $\"\"$ )

\

$\"\"$ (Simplify)

\

The equation of the axis symmetry is $\"\"$ and $\"\"$ -coordinate of the vertex is $\"\"$ . $\"\"$

\

Find the $\"\"$ -coordinate of the vertex by evaluating the function for $\"\"$ .

\

$\"\"$ (Original function)

\

$\"\"$ (Substitute $\"\"$ )

\

$\"\"$ (Evaluate powers: $\"\"$ )

\

$\"\"$ (Multiply)

\

$\"\"$ (Substitute: $\"\"$ )

\

The minimum value of the function is $\"\"$ .

\

Find domain and range of the function.

\

The domain is all real numbers.

\

The range is all real numbers greater than or equal to minimum value or $\"\"$ .

\

$\"\"$

\

The function has minimum value.

\

The minimum value of the function is $\"\"$ .

\

Domain is all real numbers.

\

The range is $\"\"$ .