Question

Find the Domain and Range of the function defined

y=-x^2 + 4x -1

I can determine the Domain, yeaaa not so much luck on finding the range >.> Thank you :)

Answer 1

so first find your vertices you know this parabaloa is pointing downwards right and your vertices is x = -b/2a its a formula i dontk now if you know that but x = -4/-2 = 2 and y = -4+8-1 =3 so therefroe range is 3 to - infinity :)

Answer 2

The answer is correct, but I'm not really familiar with the method :( Is this the only way to do it?

Answer 3

which grade are you in?

Answer 4

freshman in college :) This is from Calculus 1

Answer 5

lol alright so you should know this from advanced function, ill say it in steps

Answer 6

first thing is you NEED to draw the graph no matter what, you could either do it by finding the max/min point by finding its derivative then doing the table if its a max or a min OR my way where i knew it was a parabala so it can either be a max OR a min depending on the coeffiicent inthis case it was a negative. i suggest you do it by finding its derivative it will make sense to you a lot.

Answer 7

Well this is kinda from the first chapter I've learned, which is preliminaries but if this is the only way then I guess I'll try to comprehend. So you're implying that I should imagine this as a graph of a parabola facing downwards due to the x^2 having a negative coefficient?

Answer 8

yupp

Answer 9

Aaaaand how do I determine the range based on the graph?

Answer 10

wherever the graph is active let me show you