MATH SOLVE

3 months ago

Q:
# Please, can someone graph this for me and include a file?g(x) = x3 β x2 β 4x + 4

Accepted Solution

A:

ANSWER

See attachment

EXPLANATION

The given function is

[tex]g(x) = {x}^{3} - {x}^{2} - 4x + 4[/tex]

The y-intercept is

[tex]g(0) = 4[/tex]

To find the x-intercepts, we equate the function to zero.

[tex] {x}^{3} - {x}^{2} - 4x + 4 = 0[/tex]

Factor by grouping;

[tex] {x}^{2}(x - 1) - 4(x - 1)= 0[/tex]

[tex]( {x}^{2} - 4)(x - 1)= 0[/tex]

[tex]{x}^{2} - 4 = 0 \: or \: x - 1 = 0[/tex]

[tex]x = \pm \: \sqrt{4} \: or \: x = 1[/tex]

[tex]x = \pm \: 2\: or \: x = 1[/tex]

[tex]x = - 2\: or \: x = 1 \: or \: x = 2[/tex]

The x-intercepts are;

(-2,0),(1,0) and (2,0)

Since the polynomial has an odd degree and a positive leading coefficient, the graph will rise on the left side and also rise on the right side.

Using the intercepts and the end behavior, we obtain the graph as shown in the attachment.

See attachment

EXPLANATION

The given function is

[tex]g(x) = {x}^{3} - {x}^{2} - 4x + 4[/tex]

The y-intercept is

[tex]g(0) = 4[/tex]

To find the x-intercepts, we equate the function to zero.

[tex] {x}^{3} - {x}^{2} - 4x + 4 = 0[/tex]

Factor by grouping;

[tex] {x}^{2}(x - 1) - 4(x - 1)= 0[/tex]

[tex]( {x}^{2} - 4)(x - 1)= 0[/tex]

[tex]{x}^{2} - 4 = 0 \: or \: x - 1 = 0[/tex]

[tex]x = \pm \: \sqrt{4} \: or \: x = 1[/tex]

[tex]x = \pm \: 2\: or \: x = 1[/tex]

[tex]x = - 2\: or \: x = 1 \: or \: x = 2[/tex]

The x-intercepts are;

(-2,0),(1,0) and (2,0)

Since the polynomial has an odd degree and a positive leading coefficient, the graph will rise on the left side and also rise on the right side.

Using the intercepts and the end behavior, we obtain the graph as shown in the attachment.