Answer
The function has a minimum value.
The minimum value is $-33$.
Work Step by Step
Comparing $y=3x^{2}-24x+15$ with $ax^{2}+bx+c$, we see that $a=3$ and $b=-24$.
As $a\gt0$, the parabola opens up and the function has a minimum value. The minimum value is the y-coordinate of the vertex.
The x-coordinate of the vertex is given by
$x=-\frac{b}{2a}=-\frac{-24}{2(3)}=4$
Evaluating the function at $x=4$, we get the y-coordinate of the vertex as
$y=3(4)^{2}-24(4)+15=-33$.
