Abasketball is thrown upwards. the height f(t), in feet, of the basketball at time t, in seconds, is given by the following function: f(t) = −16t2 + 44t + 12 which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground? −0.25 < t < 2 0 < t < 3 1 < t < 2.4 1.375 < t <

let's first find the places where the ball hits the ground, that way we know how many seconds it took, let's set f(t) = 0 like before, check the picture below.

so we know the graph goes from -1/4 to 3, so the ball hits the ground on its way back down at x = 3.

now, let's find the maximum, we only need the x-coordinate from the vertex,

so, the ball reaches at maximum when x = 11/8, or 1.375, and hits the ground when x = 3.

so the domain, namely the values for x are, x ⩾ 1.375 and x ⩽ 3, or we can write it as a triplet of 1.375 ⩽ x ⩽ 3.

answer for #1 is c

answer for #2 is d

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the answer is 62.8 cubic units