Question

Pre-calculus textbook need help

Answer 1

Good question!

look at what h(x) is doing to g(x). It is multiplying it by -3, which flips the graph upside down (stretching and skewing doesnt matter much for min and max values)

so we know it is a max vs a min.

now, think about transformations? what is an equation for g(x)? it moves right one and down 2, so
$g(x) = {(x - 1)}^{2} - 2$
use what you know about composition of functions

$h(x) = - 3(g(x)) - 1 \\ h(x) = - 3( {(x - 1)}^{2} - 2) - 1 \\ h(x) = - 3 {(x - 1)}^{2} + 6 - 1 \\ h(x) = - 3 {(x - 1)}^{2} + 5$