The shape of a rollercoaster is modeled by a polynomial function, r(x). describe how to find the x-intercepts of r(x) and how to construct a rough graph of r(x) so that the engineer can predict when there will be no change in the direction of the coaster. you may create a sample polynomial to be used in your explanations.

You will need three roots for this, so we have

 Let x = -30, -10 and +20

So the factors will be  (x+30)(x+10)(x-20)

The divide it to 100, this will help bring the peak up and down

So the polynomial function R(x) will become

1/100 *  (x+30)(x+10)(x-20)

R(x) = 1/100 * (x+30)(x+10)(x-20)

Finding the X-intercept:

Let R(x) = 0 and solve for x.

1/100 * (x+30)(x+10)(x-20) = 0

x = -30, -10, 20 are the x-intercepts.

The first feature of a polynomial function is that its graph is continuous, that is, the graph of a polynomial function has no breaks. The second feature is that the graph of a polynomial function has only smooth, rounded turns.

Since the problem establishes that we may create a sample polynomial to be used in our explanations, we can say that this polynomial function is:

To find the x-intercepts of R(x) set R(x) equal to zero and solve for x, so:

So the real zeros are:

To construct a rough graph of R(x) we start setting the zeros on the x-axis. On the other hand, given that the leading coefficient is negative, that is, . The graph falls to the left and right. So the graph is shown in the Figure below.

b

step-by-step explanation: