for the graph of y^2 = ax, is it if a is 1 or 2 or wtv number it will still look the same as y^2=x

Yup! Shapes remain the same.

I have confirmed that part i is NOT in your syllabus (the component has been removed from your year onwards).

Your syllabus code for exam is 4049 and those taking O Levels this year are taking syllabus 4047. The component on "power graphs" has been removed, so there is no longer power graphs in your syllabus 4049.

what does parabola mean tho

https://en.wikipedia.org/wiki/Parabola

You can think of it as a quadratic curve at your level

i dont rly understand the "when x=5/4 and y=1/2" part onwards

Ok, this part is important for you to know.

A point lies along a line if its x coordinate and y coordinate satisfies the equation of the line.

Let’s take y = x + 1 as an example.

How do you know what points exist on the line?

Suppose x = 0. Then, what is y? If you calculate, y = 0 + 1 = 1. This means that (0, 1) is on the line.

Conversely, we can prove that (0, 1) is on the line. This is because substitution of x = 0 and y = 1 into the equation y = x + 1 yields “1 = 0 + 1”, a true statement. This means that (0, 1) is on the line.

But how about, say, (0, 5)? Is it on the same line?

Upon substitution of x = 0 and y = 5, we get “5 = 0 + 1”, which is obviously not a true statement. This means that (0, 5) is not on that line.

So, if a point lies on the line, substitution of its coordinates into the equation gets us a “correct” statement. Otherwise, the point does not lie on the line.

Now, I give you an exercise.

1. Are the points (3, 7) and (8, 10) on the line y = 2x + 1?

2. Is the origin (0, 0) on the line y = 3x - 5?

1.(3,7) yes
(8,10) no
2.no

Yup!

So here, in the question, substitution of x = 5/4 and y = 1/2 into the equation 2y = 8x - 9 gives

“2 (1/2) = 8 (5/4) - 9”

which simplifies to

“1 = 10 - 9”

which is a true statement.

This is why the midpoint of AB, which is (5/4, 1/2) lies on the line 2y = 8x - 9.