# finding equation of a parabola

• Oct 23rd 2009, 07:57 PM
flyinhigh123
finding equation of a parabola
hiii i just need some help finding the equation of a parabola that has the points (-a,0), (a,0) and (0,a/2)

this is based on a volume of revolution question,
a hemispherical bowl of radius a units is filled with water to a depth of a/2 units. find by integration the volume of the water

i just really need some help with this because i tried simultaenous equations for the equation of the parabola and i got
(-1/4)a(x^2)+(1/4)x+(a/2)
can anyone tell me if this equation is right for the parabola because i dont think it is
thankyou to anyone who can help me !! =)
• Oct 23rd 2009, 08:33 PM
Rapha
Hi.

Quote:

Originally Posted by flyinhigh123
hiii i just need some help finding the equation of a parabola that has the points (-a,0), (a,0) and (0,a/2)

this is based on a volume of revolution question,
a hemispherical bowl of radius a units is filled with water to a depth of a/2 units. find by integration the volume of the water

i just really need some help with this because i tried simultaenous equations for the equation of the parabola and i got
(-1/4)a(x^2)+(1/4)x+(a/2)
can anyone tell me if this equation is right for the parabola because i dont think it is
thankyou to anyone who can help me !! =)

Let f(x):=(-1/4)a(x^2)+(1/4)x+(a/2)

f(a) = -a^3/4+a/4+a/2 != 0

You already know that -a and +a is a zero of f, so

f(x) = (x+a)(x-a)

but f(0) should be a/2

so

f(0) = a*(-a) = -a^2

Thus something is missing

-a^2*missing = a/2

missing = -1/(2a)

Hence

f(x) = (x-a)(x+a)*[-1/(2a)]

Done

Yours
Rapha