find the equation of the parabola please

[unregistered]

So I substitute the value of the vertex in the standard form:

The first question I have is when substituting for the values of f(x) and x, would I used (0,0), or (6,0). <insert first rule here please> That is to say, is there a rule stating which should always be used? So just for the sake of getting to my next question, I used (6,0):

and then I simplify:

So when trying to find the value of a to make the equation true, I could really just put any number for a and the equation would be true which I don't think is what I'm supposed to do. <Insert next rule here> if you someone who knows a definite rule with regards to these two questions, I would be very very very thankful, grateful, beholden, appreciative.... Rules work well for my peanut sized brain.

Thanks

 

[soroban]

Hello, unregistered!

You were that close . . .

So I substitute the value of the vertex in the standard form:
\(\displaystyle f(x) \:=\:a(x\,-\,3)^2\,+\,(-9)\)

When substituting for the values of \(\displaystyle f(x)\) and \(\displaystyle x\), would I use (0,0), or (6,0)?
Yes . . . because (0,0) and (6,0) are on the parabola,
their coordinates will satisfy its equation.

Is there a rule stating which should always be used? .Either point can be used.

So just for the sake of getting to my next question, I used (6,0):
. . \(\displaystyle 0\:=\:a(6\,-\,3)^2\,+\,(-0)\)

and then I simplify: \(\displaystyle \,0\:=\:0a\) . . . no

You had: \(\displaystyle \:a(6\,-\,3)^2\,+\,(-9)\:=\:0\;\;\Rightarrow\;\;9a\,-\,9\:=\:0\;\;\Rightarrow\;\;a\,=\,1\)

 

[unregistered]

wait wait wait, lemme see if I get this straight, I'm a little slow, ate a lot of paint chips as a child. So the 2nd rule I was looking for wasn't to solve for 0 on the left like all of my problems up until now, if 0 is on the left side of the equation then disregard it altogether yes? If that's true then that's an easy rule that I can wrap my brain around.

Thank you soroban.

- nicholas

 

[unregistered]

whoops, never mind that last thing, I see what you did now and where I goofed it up. Thanks.