this question is not about solving the stated problem, but about understanding it.\na rocket is launched…

this question is not about solving the stated problem, but about understanding it.\na rocket is launched, and its height above sea level t seconds after launch is given by the equation\n$h(t)=-4.9t^{2}+1900t + 280$.\na) from what height was the rocket launched?\nto answer this question, wed find\n b) what is the maximum height th\nto answer this question, wed find\n c) if the rocket will splash down in the ocean, when will it splash down?\nto answer this question, wed find:

this question is not about solving the stated problem, but about understanding it.\na rocket is launched, and its height above sea level t seconds after launch is given by the equation\n$h(t)=-4.9t^{2}+1900t + 280$.\na) from what height was the rocket launched?\nto answer this question, wed find\n b) what is the maximum height th\nto answer this question, wed find\n c) if the rocket will splash down in the ocean, when will it splash down?\nto answer this question, wed find:

Answer

Brief Explanations:

  • For part a), when (t = 0) (at launch time), (h(0)=-4.9\times0^{2}+1900\times0 + 280). The value of (h(0)) is the (h -)intercept of the function (h(t)).
  • For part b), the function (h(t)=-4.9t^{2}+1900t + 280) is a quadratic function of the form (y = ax^{2}+bx + c) ((a=-4.9), (b = 1900), (c = 280)). The vertex of a quadratic function (y=ax^{2}+bx + c) has coordinates (\left(-\frac{b}{2a},h\left(-\frac{b}{2a}\right)\right)). The maximum (since (a<0)) height of the rocket is the (h -)coordinate of the vertex of the parabola (y = h(t)).
  • For part c), when the rocket splashes down, (h(t)=0). We need to solve the quadratic equation (-4.9t^{2}+1900t + 280=0) for (t>0). The solutions of the quadratic equation (ax^{2}+bx + c = 0) ((a=-4.9), (b = 1900), (c = 280)) are given by the quadratic formula (t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}). We are interested in the positive (t -)value, which is the (t -)intercept (where (h(t)=0) and (t>0)) of the function (h(t)).

Answer:

a) The (h) intercept. b) The (h) coordinate of the vertex. c) The (t) intercept.