Question

which way does this parabola open: x^2 = -8(y-3)

Answer 1

downward.

Answer 2

Down, because the coefficient of \(-x^2\) ends up being negative.

Answer 3

thank you! but can someone show me how to figure that out? I am completely lost :(

Answer 4

You just get it in the form \(ax^2 + bx + c = 0\)
(They don't have to be +'s, any of those can be negative)

Answer 5

Then if a is positive, it opens up, and if a is negative, it opens down.

Answer 6

In this case, you had to divide by -8 which caused a negative to show up. So it opens down.

Answer 7

how to you plot
x^2=y?
since x is the independent variable, for different values of x gives out different values of y.
so, if we take all the ordered pairs (x,y) and try plotting theses points on the y-vs-x graph, you would get a concave upward graph, with it's lowest point (0,0). This curve is called a parabola. and since it opens upward, it is called upward parabola.
If we now try to graph y=-x^2, we get a downward parabola.

Answer 8

so I am trying to get all #'s to the left of the equal sign correct? That is started by dividing both sides by -8? Or do I complete the : -8(y-3) first? I have this formula: x=(y-k)^2 + h but I don't know how to drop in the values with information I have been given. thank you !!!!

Answer 9

always try to know how we do rather than what we do.

Answer 10

Wait, are you trying to complete the square? Because you don't need to know that just to know which way the parabola opens. All you have to do to know that is solve for y.

Answer 11

no I am not trying to complete the square.. I just don't know how to find the (h,k), focus, radius, stuff like that

Answer 12

Oh! I get it now. Sorry.

Answer 13

Do you know \(4p(y-k) = (x-h)^2\)
That's basically the form the equation given was in.

Answer 14

i did not know that ! is that the best formula to attack these questions with?

Answer 15

Well especially when they give you the question in that form. And it gives you h and k right there.

To put it in that form when not given like that, you'll usually have to complete the square.

Answer 16

thank you so much! i guess i need to brush up on the completing the square :)

Answer 17

I can help you with that, too. Do you know the quadratic formula?

Answer 18

just about the only formula I do know :) so yes :)

Answer 19

You're like me, then. The good news is you can use the quadratic formula to complete the square.

Answer 20

Start with the classic
\[x = \frac{-b \pm \sqrt{(b^2 - 4ac)}}{2a}\]

Answer 21

\[x + \frac{b}{2a} = \frac{\sqrt{(b^2 - 4ac)}}{2a}\]
\[(x + \frac{b}{2a})^2 = \frac{(b^2 - 4ac)}{4a^2}\]

Answer 22

Look familiar? :D

Answer 23

the top one did :)

Answer 24

The quadratic formula is derived by completing the square, I just reversed it a little to show how it can help

Answer 25

i see.. but not really :D math is my nemesis!! lol..

Answer 26

Ok, well, you might have to brush up on it then. :P

Answer 27

I can't really teach HOW to do it... just how to do it faster. :D

Answer 28

hahah.. i appreciate all your help and i will see if i can figure this out :)

Answer 29

lol