$f(x)=2x^{2}12x-4$

$($a$)$ The function's vertex is at the point

$($Type an ordered pair, using integers or fractions $)$

$($b$)$ Determine whether the parabola has a maximum value or a minimum value and find the value. Select the correct choice below and fill in the answer box to complete your choice.

$($Type an integer or a fraction.$)$

A$.$ The parabola opens downward and has a maximum value of $$

B$.$ The parabola opens upward and has a minimum value of $$

$($c$)$ The range of $f(x)$ is $$

$($Type your answer in interval notation. Use integers or fractions for any numbers in the expression$)$

$($d$)$ The function is increasing on $$

$($Type your answer in interval notation. Use integers or fractions for any numbers in the expression.$)$

The function is decreasing on $$

$($Type your answer in interval notation. Use integers or fractions for any numbers in the expression.$)$