



 
Sure Austin. The "intersection" is where both functions have the same (t,y) variable values. This means that the y in the first function is the same as the y in the second function. Of course you know that if something1 = y and y = something2, then something1 = something2. So 4t + 300 = 4.9 (t  5)^{2} + 300 Now you can simply solve for t using any of the quadratic techniques (factoring, completing the square, quadratic formula...). 4t = 4.9 ( t^{2}  10t + 25) 4t = 4.9t^{2} + 49t  122.5 4.9t^{2}  53t + 122.5 = 0 This job is clearly one for the quadratic formula. Remember it looks like this: The "t" is the unknown, but a, b, and c are the coefficients in front of the squared, linear and constant parts. That is, a = 4.9, b = 53 and c = 122.5. That means we substitute these in: And using a calculator, we calculate that there are two values of t (because of the plus/minus): 7.47 and 3.35. I'm guessing that these are seconds, because your question looks like it is modelling motion under the influence of gravity over time. The last step is this: for EACH value of t you just plug it into the easier formula you started with to calculate y. y = 4(7.47) + 300 = 270.12 And so the intersection points are (t,y) = (7.47, 270.12) and (3.35, 286.60). Hope this helps,  


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