NEED HELP KNOWING HOW TO DO THIS PLEASE: Find the range of the function.

f(x) = (x + 5)^2 + 8

Question

NEED HELP KNOWING HOW TO DO THIS PLEASE: Find the range of the function.

f(x) = (x + 5)^2 + 8

iwanttogotostanford · Answer

@zepdrix

calculusxy · Answer

f(x) = (x + 5)^2 + 8 is in vertex form, which is y = (x - h)^2 + k 

To derive the vertex from the vertex form, you need to find what value of x can make $x + 5 = 0$. This means, that in this case, you would have the opposite of 5, which is -5 because $-5 + 5 = 0$. 

The k value is 8, so the y-coordinate of the vertex will be 8.

calculusxy · Answer

So now we know that the vertex for this quadratic is (-5, 8). Since a value in the quadratic is positive, we know that the parabola will be facing upwards. Therefore, (-5, 8) is the minimum of the parabola. 

Since we also know that the range is the y-values (outputs) and we know that the minimum output is -8, the range would be y≥8.

iwanttogotostanford · Answer

ok, im reviewing what you already wrote ! Thank you so much.  I needed immense help.  IS it ok if i tag you in others for help on knowing what to do ? This is pre-calc.

calculusxy · Answer

You're welcome. However, I need to go now. Sorry about that but good luck!

iwanttogotostanford · Answer

ok, thanks!