Given the height function below
[tex]h(t)=-4.9t^2+13t+0.5[/tex]
Let us now plot the graph of the height function of the rocket.
Y-intercept
The point where a line or curve crosses the y-axis of a graph.
Therefore, the y-intercept of the function is 0.5m, which represents the constant value of rocket height.
Roots of the function
The roots of a function are the x-intercepts, which is the y-coordinate of points lying on the x-axis is zero.
Therefore, the roots of the function are
[tex](-0.038secs,2.691secs)[/tex]
which represents the time at which the rocket is initially launched and the time at which the function hits the ground.
Vertex of the function
The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.
Therefore, the vertex of the function is
[tex](1.327secs,9.122m)[/tex]
which represents the maximum time and height of the rocket.
