graph the polynomial funtion, f(x)=3x^2(x-1)(x-2)

Question

show me how to solve this.

Answer 1

The polynomial f (x ) = 3x ²(x - 1)(x - 2)

1) Zeros f (x ) = 3x ²(x - 1)(x - 2) using zeros to graph the polynomial.

 3x ²(x - 1)(x - 2) = 0

 3x ² = 0 , (x - 1) = 0 and (x - 2) = 0

x  = 0 , x  = 1 ,  x = 2.

Real zeros are x  intercepts of the graph.

2)Test points

Make the table of values to for the polnomial.

Here i test 3 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 = 3x2(x - 1)(x - 2)	(x, y )
- 0.5	y = 3(- 0.5)2 (-0.5 - 1) (-0.5-2) = 2.8	(- 0.5, 2.8)
0	y = 3(0)2 (0 -1) (0-2) =  0	(0, 0)
0.5	y = 3( 0.5)2 (0.5 - 1) (0.5-2) = 0.56	(0.5, 0.56)

3) End behavior f (x ) = 3x ²(x - 1)(x - 2)

f (x ) = 3x ⁴ - 9x ³ + 6x ²

Degree of polynomial is 4 and leading coefficient 3.

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

All even degree polynomials behave on thier ends like quadratics.

All even degree polynomials are either up on both ends and or down on both ends.depending on whether the polynomial has, respectively, a positive or negative leading coefficient.

The above polynomial even degree  polynomial with a positive leading coefficient .

So the graph up on both ends.

4)Graph

1.Draw a coordinate plane.

2.Plot the  intercepts coordinate points found in the table.

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