Classify the conic section and write it's equation in standard form.
-x^2 + 10x + y -21=0

This is a parabola but I don't know why and also I need help on making it into standard form.

Question

Classify the conic section and write it's equation in standard form. 
-x^2 + 10x + y -21=0

This is a parabola but I don't know why and also I need help on making it into standard form.

superhelp101 · Answer

@turningtest

jhannybean · Answer

It's a parabola because you've got an $x^2$ term, which implies a quadratic equation.

superhelp101 · Answer

@turingTest

superhelp101 · Answer

My teachers got y=(x-5)^2 -4

superhelp101 · Answer

I don't really understand the steps

superhelp101 · Answer

Actually Ohhh u completed the square

anonymous · Answer

Put all the y's on one side, and all the x's and constants on other side

anonymous · Answer

Then do some factoring

jhannybean · Answer

Hmm,let's try this agani.

jhannybean · Answer

Oh, I see. $$-x^2 + 10x + y -21=0\implies -y = -x^2 +10x-21 \implies y=x^2 -10x+21$$

jhannybean · Answer

Then... $$y=x^2-10x+21$$$$y=(x^2-10x)+21$$$$y=(x^2-10x+25-25)+21-25$$$$y=(x-5)^2 -4$$

jhannybean · Answer

I completed the square to find my parabola in vertex form.

superhelp101 · Answer

So did we basically complete the square twice in the problem?

jhannybean · Answer

Twice? The first time I messed up.

jhannybean · Answer

Just look at the last portion :)

superhelp101 · Answer

Oh alright that makes sense! Thank you! If I have any other questions I will ask u :)

jhannybean · Answer

Sure thing :) I will try.