Question

The graph shows a coordinate plane that extends from negative 8 to 8 in each direction. There are three movable points, one at ( negative 2 , 0 ), one at ( 0 , 0 ), and one at ( 2 , 0 ), as well as a parabola passing through the three points. Drag the points to create a graph that satisfies the following requirements: Domain: -4 < x < 2 Range 0 < y < 4

Answer 1

The cubic polynomial function is y = x³ - 4x and the graph that satisfies the given requirements can be seen in the image attached below.

How to graph polynomial functions.

To graph the polynomial function with the given points (-2,0), (0,0) and (2,0), we need to locate the points on the graph.

After that, we are told that the parabola pass through these three points, that is an hint to let us know that this is a cubic polynomial function and the highest power for the leading term will be raised to power 3.

Also, this polynomial function must satisfies the:

Domain: - 4 < x < 2

Range: 0 < y < 4

The possible cubic polynomial that satisfies this constraint will be;

y = ax³ + cx

Using the given points (-2,0) , (0,0), and (2,0).

When, x = -2

y = -2³a + -2c

y = -8a - 2c

when x = 0, y = 0

when x = 2

y = 2³a + 2c

y = 8a + 2c

Adding the equations together, we have y = -8a -2c + 0 + 8a + 2c = 0. This shows that there are many possible solution to this polynomial. But suppose we set a = 1 and c = -4, which satisfies the domain and the range of the function. And we plug it into y = ax³ + cx.

Then, the cubic polynomial function becomes:

y = x³ - 4x.