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An Labrador leaps over a hurdle. The function f(t) represents the height of the Labrador above the ground, in inches, at t seconds:
f(t) = -16t2 + 26t
A foxhound jumps over the same hurdle. The table shows the height of the foxhound above the ground g(t), in inches, at t seconds:
Time (t) g(t)
Part A: Compare and interpret the maximum of f(t) and g(t)? (4 points)
Part B: Which function has a greater x-intercept? What do the x-intercepts of the graphs of f(t) and g(t) represent? (4 points)
Part C: Determine the y-intercepts of both functions and explain what this means in the context of the problem. (2 points)
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Part a) the max of g(t) occurs when t=0.6 seconds, for f(t) since the parabola is concave down due to the negative sign then we know that there is a max on the parabola, the max for f(t) occurs at (13/16,169/16) 169/6=10.5625inches at time 0.8125seconds
Part b) f(t) has greater x intercepts, meaning that when the labrador will land later than the fox when it jumps over the hurdle
y intercepts represents that height for where they start
which is 0 for g(t)
and for f(t) it is 15.6