Posted by **Erica** on Friday, August 31, 2012 at 10:41am.

the dome over a town hall has a parabolic shape. the dome measures 48 m across and rises 12m at the centre. A vertical column needs to be attached to the dome at a point that is 4m away from its rim. How tall is the dome at this point? Also, what is the equation that models the shape of this dome?

- math -
**MathMate**, Friday, August 31, 2012 at 11:15am
Take the vertex of the parabola at x=0.

Then the equation of the parabola (opening downwards) is y=12-ax^2 where a is a constant to be found.

We know that y=0 at x=±24 (half span), so

0=12-a(24^2)

=>

a=12/576=1/48

The equation of the parabola is therefore

y=12-x^2/48.

I will let you finish the problem.

- math -
**Erica**, Friday, August 31, 2012 at 11:23am
all these numbers kind of confuse me. Im not sure what ^ means. Right now the only equation i have learned is y= a(x-s)(x-t)

- math -
**MathMate**, Friday, August 31, 2012 at 11:39am
x^2 means x squared, or x².

If you just started with parabolas, it won't hurt to say what you've learned so far.

Let's start over:

We first assume the vertex of the parabola is at x=0.

We know that y=0 at x=±24, or

y=a(x-24)(x+24).

We also know that y=12 at x=0, i.e.

12=a(0-24)(0+24)=-576

so a=12/(-576)=-1/48

The equation of the parabola is therefore:

y=(x-24)(x+24)/48

Can you then continue?

- math -
**MathMate**, Friday, August 31, 2012 at 11:41am
Correction to one of the above lines:

12=a(0-24)(0+24)=-576**a**

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