Solve each equation by graphing -x^3-3x-2=0

2 Answers

The cubic function y = - x³ - 3x - 2

Find the y - intercept by substituting x = 0 in the given equation.

y = - 0³ - 3(0) - 2

y = - 2

The y - intercept is - 2.

Test points

Make the table of values for the polynomial.

Here i test 4 points to determine whether the graph of polynomials lies above or below the x axis.

Choose values for x and find the corresponding values for y .

x	y = - x³ - 3x - 2	(x, y )
-0.5	y = - (- 0.5)³ - 3(- 0.5) - 2 = - 0.375	(- 0.5, -0.375)
-1	y = - (- 1)³ - 3(- 1) - 2 = 2	(-1, 2)
0.5	y = - ( 0.5)³ - 3( 0.5) - 2 = -3.375	(0.5, -3.375)
1	y = - (1)³ - 3(1) - 2 = -6	(1, -6)

End behavior y = - x³ - 3x - 2

Degree of the polynomial is 3 and leading coefficient - 1.

The graph of a polynomial function is always a smooth curve; that is, it has no breaks or corners.

All odd degree polynomials behave on their ends like cubics.

All odd degree polynomials have ends that head off in opposite directions.depending on whether the polynomial has, respectively, a positive or negative leading coefficient.

The above polynomial odd degree polynomial with a negative leading coefficient .

So the graph falls to the right and rises to the left.

1.Draw a coordinate plane.

2.Plot the y intercept and coordinate points found in the table.

3.Then sketch the graph, connecting the points with a smooth curve.

Graph :