Consider the given function $p(x)=-2x^2+6x+9$

$($a$)$ Write the function in vertex form.

$($b$)$ Identify the vertex.

$($c$)$ Determine the $x-$intercept$($s$).$

$($d$)$ Determine the $y-$intercept$($s$).$

$($e$)$ Sketch the function.

$($f$)$ Determine the axis of symmetry.

$($g$)$ Determine the minimum or maximum value of the function.

$($h$)$ Write the domain and range in interval notation.

Write your answers as integers or simplified fractions.