The "hang time" of a football is the amount of time the football stays in the air after being kicked. The height, in meters, of the football above the ground at time t can be modeled by the quadratic function: h(t)=-4.9t^(2)+19.6 t Which of the following equivalent expressions displays the hang time of the football as a constant or coefficient? Choose 1 answer: (A) -4.9(t-2)^(2)+19.6 (B) -4.9 t(t-4) (C) -4.9(t-3)^(2)-9.8 t+4 (D) -4.9(t-1)^(2)+9.8 t+4.

Question

The "hang time" of a football is the amount of time the football stays in the air after being kicked. The height, in meters, of the football above the ground at time  t can be modeled by the quadratic function:  h(t)=-4.9t^(2)+19.6 t Which of the following equivalent expressions displays the hang time of the football as a constant or coefficient? Choose 1 answer: (A)  -4.9(t-2)^(2)+19.6 (B)  -4.9 t(t-4) (C)  -4.9(t-3)^(2)-9.8 t+4 (D)  -4.9(t-1)^(2)+9.8 t+4.

Bytelearn · Accepted Answer

Step 1: Option (A) Expansion: The given function for the height of the football is h(t) = -4.9t^2 + 19.6t. We need to find an equivalent expression that displays the hang time as a constant or coefficient. To do this, we will look at each option and see if it can be rearranged or simplified to show the hang time in the desired form.Step 2: Option (B) Expansion: Let's start with option (A): -4.9(t-2)^2 + 19.6. We can expand this expression to see if it simplifies to the original function. Expanding (t-2)^2 gives t^2 - 4t + 4. Multiplying by -4.9 gives -4.9t^2 + 19.6t - 19.6. Adding 19.6 to this expression does not give us the original function, so option (A) is not equivalent to the original function.Step 3: Option (C) Expansion: Next, we consider option (B): -4.9t(t-4). Expanding this expression gives -4.9t^2 + 19.6t. This is exactly the original function, so option (B) is equivalent to the original function. However, it does not display the hang time as a constant or coefficient.Step 4: Option (D) Expansion: Now, let's look at option (C): -4.9(t-3)^2 - 9.8t + 4. Expanding (t-3)^2 gives t^2 - 6t + 9. Multiplying by -4.9 gives -4.9t^2 + 29.4t - 44.1. Adding -9.8t + 4 to this does not simplify to the original function, so option (C) is not equivalent to the original function.Finally, we examine option (D): -4.9(t-1)^2 + 9.8t + 4. Expanding (t-1)^2 gives t^2 - 2t + 1. Multiplying by -4.9 gives -4.9t^2 + 9.8t - 4.9. Adding 9.8t + 4 to this expression gives us -4.9t^2 + 19.6t, which is the original function. However, this expression also does not display the hang time as a constant or coefficient.

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