Answer
a. $f(x) = 3(x-2)^2 +1$
b. See graph attached below
c. Minimum value = 1
Work Step by Step
$f(x) = 3x^2 -12x + 13$
a. $f(x) = 3( x^2 -4x + 4) + 13 - 3(4)$
$f(x) = 3(x-2)^2 +1$
b. See graph attached below
c. The minimum value is at the vertex, which is at (2, 1) (from standard form)
Minimum value = 1