# Rearranging equation from graph

• Aug 29th 2011, 07:51 AM
asdf51
Rearranging equation from graph
Hi,

I am having some (major) problems trying to rearrange an equation which defines a line on a graph- which Excel produced. They are in the format y=(-ax^2)+bx. I am trying to rearrange the equation to give x=.....

The two equations are as follows.

y= -0.4615x^2+29.381x in other words y = (-0.4615*x^2) + (29.381*x)

y= -0.7565x^2+41.689x in other words y= (-0.7565*x^2) + (41.689*x)

Unfortunately, my ability does not extend beyond putting the brackets in, and despite numerous attempts, I cannot work out how to calculate x.

If anyone is able to help, it would be fantastic!

Thanks
• Aug 29th 2011, 08:24 AM
e^(i*pi)
Re: Rearranging equation from graph
Quote:

Originally Posted by asdf51
Hi,

I am having some (major) problems trying to rearrange an equation which defines a line on a graph- which Excel produced. They are in the format y=(-ax^2)+bx. I am trying to rearrange the equation to give x=.....

The two equations are as follows.

y= -0.4615x^2+29.381x in other words y = (-0.4615*x^2) + (29.381*x)

y= -0.7565x^2+41.689x in other words y= (-0.7565*x^2) + (41.689*x)

Unfortunately, my ability does not extend beyond putting the brackets in, and despite numerous attempts, I cannot work out how to calculate x.

If anyone is able to help, it would be fantastic!

Thanks

Take y from both sides: $\displaystyle -0.4615x^2+29.381x-y = 0$

Use the quadratic formula to find x in terms of y. If you want to find the roots of the equation then y=0 and you can factor.

Spoiler:

$\displaystyle x = \dfrac{-29.381 \pm \sqrt{29.381^2 + 4 \times 0.4615 \times y}}{2 \times -0.4615}$
• Aug 29th 2011, 10:09 AM
asdf51
Re: Rearranging equation from graph
Quote:

Originally Posted by e^(i*pi)
Take y from both sides: $\displaystyle -0.4615x^2+29.381x-y = 0$

Use the quadratic formula to find x in terms of y. If you want to find the roots of the equation then y=0 and you can factor.

Spoiler:

$\displaystyle x = \dfrac{-29.381 \pm \sqrt{29.381^2 + 4 \times 0.4615 \times y}}{2 \times -0.4615}$

Thanks for the reply. However, I can't seem to get it to work.

If y=-0.4615*(x^2)+29.381*x, and x=20, then y=403.02.

However, using the equation you gave, if you use 403 as the y value, then I cannot get 20 as the value for x.

Am I just being stupid here or what!?

Thanks!(Happy)
• Aug 31st 2011, 03:07 PM
asdf51
Re: Rearranging equation from graph
Just wondering if anyone is able to help here- I still cannot work it out!

Thanks :)