Question

Finding the fiction y intercept roots vertex and the sketch of fiction to explain what each points tells about the rocket

Answer 1

Given the height function below

`h(t)=-4.9t^2+13t+0.5`

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

`(-0.038secs,2.691secs)`

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

`(1.327secs,9.122m)`

which represents the maximum time and height of the rocket.