math
posted by Erica on .
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?

Take the vertex of the parabola at x=0.
Then the equation of the parabola (opening downwards) is y=12ax^2 where a is a constant to be found.
We know that y=0 at x=±24 (half span), so
0=12a(24^2)
=>
a=12/576=1/48
The equation of the parabola is therefore
y=12x^2/48.
I will let you finish the problem. 
all these numbers kind of confuse me. Im not sure what ^ means. Right now the only equation i have learned is y= a(xs)(xt)

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(x24)(x+24).
We also know that y=12 at x=0, i.e.
12=a(024)(0+24)=576
so a=12/(576)=1/48
The equation of the parabola is therefore:
y=(x24)(x+24)/48
Can you then continue? 
Correction to one of the above lines:
12=a(024)(0+24)=576a