Quadratic equations are used for many applications. The formula to solve quadratic equations can be used to solve all quadratic equations, even those that cannot be factored. A common application of quadratic equations is the height of a thrown object over time, which takes the earth's gravity and the velocity of the throw into account. For example, if someone throws a ball down from a height of 100 meters, the ball's distance from the ground can be modeled by the equation: d = − 9.8 t 2 − 15 t + 100 where t is the time in seconds and d is the distance in meters. At what time (t) will the ball hit the ground? (Hint: what does this mean for d=distance?) You will get two answers. Do both make sense? (Explain in detail Why or Why not).

Question

Quadratic equations are used for many applications. The formula to solve quadratic equations can be used to solve all quadratic equations, even those that cannot be factored. A common application of quadratic equations is the height of a thrown object over time, which takes the earth's gravity and the velocity of the throw into account. For example, if someone throws a ball down from a height of 100 meters, the ball's distance from the ground can be modeled by the equation: d = − 9.8 t 2 − 15 t + 100 where t is the time in seconds and d is the distance in meters.

  1. At what time (t) will the ball hit the ground? (Hint: what does this mean for d=distance?)
  2. You will get two answers. Do both make sense? (Explain in detail Why or Why not).

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