Question

trying to help someone calculate the range of a function manually. having some trouble understanding this solution.

Answer 1

Please do not comment unless you are making a serious attempt to help.

Answer 2

@SmokeyBrown would you mind looking at this, I'm a little lost

Answer 3

I'm not too sure about how they find the discriminant from the simplified equation; is that they part that's confusing?
As for the other parts, it looks like algebra for the rewriting/simplification and the quadratic formula in the last part to get the solution.
I can do some research on discriminants to see if that helps make sense of it at all

Answer 4

I think I sort of understand it now

They solve for x in terms of y

Doing that gives you sqrt(y^2-44y+4) as part of the solution

solving that for sqrt(y^2-44y+4) >= 0 gives you the possible range values for y

Answer 5

Yeah, that part makes sense, but I'm still a bit confused about how they get the
\[y ^{2}-44y+4\]
part to begin with. The only information I could find about discriminants was the formula
\[b ^{2} -4ac\]
but that only works for quadratic equations of the form
\[ax ^{2} +bx+c = 0\]
Which isn't what we're given here...

But if it makes sense to you, then I'm satisfied! :)

Answer 6

The problem doesn't say they have to solve it manually so I might just recommend them using a graph for the range parts

Answer 7

Dunno if it helps, but the equation looks like that when it's graphed out

Answer 8

I mean it's almost all real values there's just this one spot where it's undefined

Answer 9

I mean, one small range of y-values where the function doesn't reach

Answer 10

Right, I guess that's the gap between 22 + 4*sqrt(30) and 22 - 4*sqrt(30)?
So yeah, maybe the graph is helpful, if you can use it to pinpoint that range with accuracy. A little hard to see just by eye, might be easier to just solve the equation after all in this case