Re: Understanding Parabola's

There are infinitely many of course. One such would be y=4-x^2

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

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

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

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

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

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

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

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

where $\displaystyle a = \frac1{4p}$ is a constant. Choose any nonzero value for $\displaystyle a$ and you will get a parabola with a vertex at (0, 4). For the parabola to open downward, choose $\displaystyle a<0.$

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!!!!