Find the point of intersection.
(-9/100)(x-10)^2+9=(-1/24)(x-12)^2+6
I got (16.6,0.04).
2 answers
I get (0,0) and (16.552,5.136) - that's (480/29,4320/841)
If you want the "point" of intersection you must have started with
y = (-9/100)(x-10^2 + 9
and
y = (-1/2)(x-12)^2 + 6
resulting in your equation , which is solved for x
testing your result, I subbed in x = 16.6 into the left and right side , and I should have gotten .04
I got LS = 5.14
and RS = 5.12
so your answer is incorrect, but I can see what you did, so ...
multiply each side by 600
-54(x-10)^2 + 5400 = -25(x-12)^2 + 3600
-54x^2 + 1080x - 5400 + 5400 = -25x^2 + 600x - 3600 + 3600
-29x^2 + 480x = 0
-x(29x - 480) = 0
x = 0 or x = 480/29
if x=0, then y = 0
if x = 480/29, or x = appr 16.55 , then y = appr 5.14
So the points of intersection are
(0,0) and appr (16.55 , 5.14)
Here is what happened:
http://www.wolframalpha.com/input/?i=%28-9%2F100%29%28x-10%29%5E2%2B9%3D%28-1%2F24%29%28x-12%29%5E2%2B6+
y = (-9/100)(x-10^2 + 9
and
y = (-1/2)(x-12)^2 + 6
resulting in your equation , which is solved for x
testing your result, I subbed in x = 16.6 into the left and right side , and I should have gotten .04
I got LS = 5.14
and RS = 5.12
so your answer is incorrect, but I can see what you did, so ...
multiply each side by 600
-54(x-10)^2 + 5400 = -25(x-12)^2 + 3600
-54x^2 + 1080x - 5400 + 5400 = -25x^2 + 600x - 3600 + 3600
-29x^2 + 480x = 0
-x(29x - 480) = 0
x = 0 or x = 480/29
if x=0, then y = 0
if x = 480/29, or x = appr 16.55 , then y = appr 5.14
So the points of intersection are
(0,0) and appr (16.55 , 5.14)
Here is what happened:
http://www.wolframalpha.com/input/?i=%28-9%2F100%29%28x-10%29%5E2%2B9%3D%28-1%2F24%29%28x-12%29%5E2%2B6+