Find the point of intersection.
(-9/100)(x-10)^2+9=(-1/24)(x-12)^2+6
I got (16.6,0.04).
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+
To find the point of intersection between the two given equations, we need to solve the equation for x.
Let's start by simplifying the equation:
(-9/100)(x-10)^2 + 9 = (-1/24)(x-12)^2 + 6
Expand the squares:
(-9/100)(x^2 - 20x + 100) + 9 = (-1/24)(x^2 - 24x + 144) + 6
Distribute the fractions:
(-9/100)x^2 + (9/100) * 20x - (9/100) * 100 + 9 = (-1/24)x^2 + (1/24) * 24x - (1/24) * 144 + 6
Simplify further:
(-9/100)x^2 + (9/5)x - 9 + 9 = (-1/24)x^2 + x - 6 + 6
Combine like terms:
(-9/100)x^2 + (9/5)x = (-1/24)x^2 + x
Now, we'll move all terms to one side of the equation to set it equal to zero:
(-9/100)x^2 + (-1/24)x^2 + (9/5)x - x = 0
Combining like terms:
(-9/100 - 1/24)x^2 + (9/5 - 1)x = 0
Simplify further:
(-216/2400 - 100/2400)x^2 + (216/240)x = 0
Combine like terms:
(-316/2400)x^2 + (216/240)x = 0
Now, to solve for x, we can factor out the common factors:
((316/2400)x)((-1/8)x + 9/10) = 0
Now, either (316/2400)x = 0 or (-1/8)x + 9/10 = 0.
For the first equation, (316/2400)x = 0, x would only be 0.
For the second equation, (-1/8)x + 9/10 = 0, we can solve for x:
(-1/8)x = -9/10
x = (-9/10) * (8/-1)
x = 72/10
x = 7.2
So the point of intersection is approximately (7.2, 0).
It seems like the point (16.6, 0.04) was not obtained as the point of intersection. Double-check your calculations to ensure accuracy.