We are given two points on this quadratic equation: (0,42) and (3,96), which the latter point is the vertex of the quadratic equation. If we use the vertex form of the quadratic equation: y = a(x-h)^2 + k, where (h,k) is the point (3,96), we can write part of the equation:
y = a(x-3)^2 + 96
However, we do not know the value for a, but since the point (x,y) = (0,42) is on the parabola, we can replace this in the model we just found and solve for a:
42 = a(0-3)^2 + 96
-54 = a(-3)^2
-54 = 9a -----> a = -6. Therefore, the quadratic function is y = -6(x-3)^2 + 96
Once you graph the quadratic function, the time it takes the rocket to reach the ground is the intersection of the graph with the x-axis. You can use the drawn graph to estimate or you can set the above equation equal to 0 and solve for the positive value of x (in this case, x = 7).
