Interpreting equations graphically (example 2)

let f of t equal e to the 2t minus 2t squared and H of T equal 4 minus 5t squared the graphs of y equals f of T and y equals H of T are shown below so y equals f of T is here in green so this is really y is equal to e to the 2t minus 2t squared and we see f of T right over there and Y is equal H of T is shown in yellow all right now below that they say which of the following appear to be solutions of e to the 2t minus 2t squared equals 4 minus 5t squared select all that apply and I encourage you to pause the video and try to think about it now the key here is to realize that e to the 2t minus 2t squared that was F of T and thought four minus 5t squared is H of T so another way of thinking about it select all of the all of the T's for which f of T for which F of T is equal to H of T so all of the T's where F of T is equal to H of T well that's going to happen at the points of intersection so for example at t1 we see at this point right here t1 y1 so this tells us F of T 1 is equal to H of T 1 which is equal to y1 so f of T is going to be equal to H of T at T is equal to t1 now we see that there cuz it's a point of intersection now let's keep on going well they have another point of intersection right over here at T for T the cot of T 4 y 4 if you took F of T 4 you're going to get Y 4 or if you take H of T 4 you're going to get Y 4 so f of T 4 is equal to H of T 4 F of T 4 is equal to H of T 4 so if you took eetu the two times T sub 4 minus 2 T sub 4 squared and all the way that's going to be equal to 4 minus 5 times T sub 4 squared so T sub 4 since it satisfies both F since F of T and H of T equal each other when T is equal to T sub for these two things are going to equal each other when T is equal to T sub before and those are the only ones that are at a point of that are at a point of intersection and so I think we I think we are not I can check my answer and got it right