Question

this question is not about solving the stated problem, but about understanding it. a rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t)=-4.9t^{2}+1500t + 560. a) from what height was the rocket launched? to answer this question, wed find: select an answer b) what is the maximum height to answer this question, wed f c) if the rocket will splash dow to answer this question, wed f submit question the t intercept the h intercept the t coordinate of the vertex the h coordinate of the vertex

Explanation:

Step1: Understand launch - height concept

The height of the rocket at launch is when \(t = 0\). Substituting \(t=0\) into the height - function \(h(t)=-4.9t^{2}+1500t + 560\) gives the \(h\) - intercept.

Step2: Analyze maximum - height concept

The function \(h(t)=-4.9t^{2}+1500t + 560\) is a quadratic function in the form \(y = ax^{2}+bx + c\) (\(a=-4.9\), \(b = 1500\), \(c = 560\)). The maximum of a quadratic function \(y=ax^{2}+bx + c\) occurs at \(t=-\frac{b}{2a}\), and the maximum height is the \(h\) - value at this \(t\) - value, which is the \(h\) - coordinate of the vertex.

Answer:

a) The h intercept
b) The h coordinate of the vertex