Answer:
a) The initial height of the rock is of 48 feet.
b) It takes 1 seconds for the rock to reach maximum height.
c) The rock's maximum height is 50 feet.
d) It takes 6 seconds for the rock to land on the ground.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
It's vertex is the point
In which
If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that , given by the following formulas:
In this question:
The height of the ball after t seconds, in feet, is given by:
Which is a quadratic equation with
a) What is the initial height?
This is . So the initial height of the rock is of 48 feet.
b) How many seconds does it take to reach the maximum height?
This is the value of t at the vertex. So
It takes 1 seconds for the rock to reach maximum height.
c) What is the rock's maximum height?
This is the height of the ball after 1 second. So
The rock's maximum height is 50 feet.
d) How many seconds does it take to for the rock to land on the ground?
This is t for which , so we solve the quadratic equation.
Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.