Which of the following polynomial functions can be used to model the height of a ball thrown into the air?
Question
Which of the following polynomial functions can be used to model the height of a ball thrown into the air?
Solution
The height of a ball thrown into the air can be modeled by a quadratic function. This is because the motion of a thrown ball follows a parabolic path, which is the graph of a quadratic function.
A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
In the context of the height of a thrown ball:
- x represents the time since the ball was thrown
- f(x) represents the height of the ball at time x
- a is a negative constant because the ball is slowing down as it rises and speeding up as it falls (due to gravity)
- b represents the initial upward velocity of the ball
- c represents the initial height of the ball (i.e., the height from which it was thrown)
So, any polynomial function of degree 2 (a quadratic function) can be used to model the height of a ball thrown into the air, as long as the coefficient of the x^2 term is negative (to account for the effect of gravity).
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