I wasn’t here for this lesson and im lost

Step-by-step explanation:

The equation written just below Q8 is the vertex form, which makes it easy to know about the vertex of a parabola, which is the point where it changes direction, its max or min. "a" represents a constant (irrelevant to vertex but important later), "h" is the x position of the vertex (you flip the sign of h when putting it in an equation), and "k" is the y position of the vertex.

First thing's first, you want to plug in your desired vertex values: h = 4 & k = 5, so y = a(x - 4)^2 + 5 (notice sign flip!)

Then, you want to find a so that the y value is 2 when x is 1, so plug those values in and solve for a.

2 = a(1 - 4)^2 +5 (substitution)

2 = a(9) + 5 (simplification)

-3 = 9a (subtracting 5 from both sides and re-writing)

-3/9 = a (divide both sides by 9)

-1/3 = a (simplify the fraction.

Plug this into your equation and your final answer should be y = -1/3(x - 4)^2 + 5

Let me know if you need more of an explanation! I know how hard it can be to get math if you were absent when it was taught, and I hope it goes well.