Let’s first start with what is the parent function of a quadratic: f(x) = x^2.
Then, to get to x^2 + 1, the parent function was basically moved up by 1 on a graph.
To go from that equation to the h(x) function just follow the rules. Anything inside of a parentheses followed by a square is the opposite of what it actually is. So if you have (x - 8)^2, you’re moving the parent function 8 units to the right, instead of the left. If it’s (x + 8)^2, you are moving to the left 8. Anything outside of the parentheses that is being subtracted or added is moving the parent function down or up, respectively. Therefore, when it tells you + 5 at the end, that just means, up 5. Then if there is a negative out in front of the entire equation like you see there, it is being reflected over the x - axis. Then, the number being multiplied—in this case 3/4– is either a vertical compression or a vertical stretch. If the number is bigger than 1, it is a vertical stretch. If the number is smaller than one, it is a vertical compression.
All in all:
Vertical compression of 3/4
Vertical translation 4 units up
Reflection across the x - axis
Horizontal translation 8 units right
If you’re confused on anything, send me a comment or PM :)