How do you set up an equation to find a parabola? I have two given points but I don't know what I'm supposed to be doing? Help Please?

Question

anonymous · Answer

@phi could you help please?

anonymous · Answer

@ganeshie8

anonymous · Answer

@Hero

hero · Answer

What are the two given points?

hero · Answer

@huntingman15

anonymous · Answer

(3,0) and (-3,0)

hero · Answer

Those are the zeroes of the parabola. In other words:

x = 3
x = -3

Place everything on the same side to get:
x - 3 = 0
x + 3 = 0

Multiply (x - 3)(x + 3) to get the parabola expression.

anonymous · Answer

Is that all I have to do?

hero · Answer

Make sure it is in the form y = f(x) when you are finished.

anonymous · Answer

Im sorry. Ive been working all day on homework so I a little brain dead. If you multiplied (x-3) (x+3) you would get x squared + -9?

hero · Answer

$(x + 3)(x - 3) = x^2 - 9$

Recall difference of squares rule:
$(a + b)(a - b) = a^2 - b^2$

anonymous · Answer

I hate to keep bothering you but what would be my next step be then? I don't understand what the difference of squares rule is for?

hero · Answer

It's so that you can multiply $(x + 3)(x - 3)$ in one step. 

You express the final result as $y = x^2 - 9$

anonymous · Answer

Wow. Okay. I understand now. Thank you so much!

hero · Answer

Use the tagging feature if I don't respond promptly @Hero

hero · Answer

And you're welcome