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Step-by-step explanation:
On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).
now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is , where (p,q) is the turning point. now we substitute the turning point
, now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.
0 = a(3.15 - 0.76)^2 + 57
-57 =a(2.39)^2
-57 = a(5.7121)
-57/5.7121 =a
-9.9788169 = a then we substitute a to get the quadratic equation therefore f is