Understanding Parabola's

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June 15th 2012, 07:50 AM
BetterAtScience

Understanding Parabola's

I come to you with the need for some help....I'm an online student and have no assistance from the book in regards to this question;
Write an equation for a parabola that opens downward and has a vertex of (0,4)....as you see from my name this subject is not my strong suit....

My answer to this problem is simply y=0.0x-1.5 (I really don't feel to strongly that this is correct) thus is why I am here!

Thanks,
BAS
June 15th 2012, 08:07 AM
biffboy

Re: Understanding Parabola's

There are infinitely many of course. One such would be y=4-x^2
June 15th 2012, 08:29 AM
Reckoner

Re: Understanding Parabola's

Quote:

Originally Posted by BetterAtScience

I come to you with the need for some help....I'm an online student and have no assistance from the book in regards to this question;
Write an equation for a parabola that opens downward and has a vertex of (0,4)....as you see from my name this subject is not my strong suit....

My answer to this problem is simply y=0.0x-1.5 (I really don't feel to strongly that this is correct) thus is why I am here!

In general, a parabola with a vertical axis is given by the equation

$(x - h)^2 = 4p(y-k)$

where $(h, k)$ is the vertex and $p$ is the directed distance from the vertex to the focus.

We want a vertex of (0,4), so substitute these values for $h$ and $k$ :

$(x - 0)^2 = 4p(y-4)$

$\Rightarrow x^2 = 4p(y - 4)$

$\Rightarrow y = \frac1{4p}x^2 + 4$

$\Rightarrow y = ax^2 + 4,$

where $a = \frac1{4p}$ is a constant. Choose any nonzero value for $a$ and you will get a parabola with a vertex at (0, 4). For the parabola to open downward, choose $a<0.$
June 15th 2012, 09:16 AM
BetterAtScience

Re: Understanding Parabola's

That seems to make is a little clearer, I appreciate the assistance....I feel ackward asking for help since I already have Nursing degree and decided to go back to school this summer as sort of a mid-life crisis! Thank you for being here.....if you got a illness I can return the favor!!!!