Answer
a. $f(x) = 5(x+3)^2 - 41$
b. See graph attached below
c. Minimum value = -41
Work Step by Step
$f(x) = 5x^2 + 30x + 4$
a. $f(x) = 5( x^2 + 6x + 9) + 4 - 9(5)$
$f(x) = 5(x+3)^2 - 41$
b. See graph attached below
c. The minimum value is at the vertex, which is at (-3, -41) (from standard form)
Minimum value = -41
