Which of the following matches the graph of f (x) = 2(x – 1)2(x + 1)(x + 2)?

Polynomial going down from the left and passing through the point negative 2 comma 0 and going to a local minimum and then going up through the point negative 1 comma 0 to a maximum and then going down through the point 4 comma 0 to a minimum at 1 comma 0 and then going up to the right
Polynomial going down from the left and passing through the point negative 2 comma 0 and going to a local minimum and then going up to a local maximum at the point negative 1 comma 0 and then down through the point 0 comma negative 4 to a local minimum and then up through the point 1 comma 0 to the right
Polynomial going down from the left and passing through a local minimum at the point negative 1 comma 0 and going up through the point 0 comma 4 to a local maximum and then down through the point 1 comma 0 to a local minimum and then up through the point 2 comma 0 to the right
Polynomial going down from the left and passing through the point negative 1 comma 0 to a local minimum and then going up through the point 0 comma negative 4 to a local maximum at the point 1 comma 0 and then down to a local minimum and then up through the point 2 comma 0 to the right

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MrRoyal MrRoyal · Answer 1 · 2022-03-07T10:20:47+01:00

Graphs are used to represent functions, equations and polynomials

The equation of the function is given as:

[tex]f(x) = 2(x - 1)(x + 1)(x + 2)[/tex]

Set x = 0

[tex]f(0) = 2(0 - 1)(0 + 1)(0 + 2)[/tex]

[tex]f(0) = -4[/tex]

The above means that the graph passes through the point (0,-4)

Next, set f(x) to 0

[tex]2(x - 1)(x + 1)(x + 2) = 0[/tex]

Divide through by 2

[tex](x - 1)(x + 1)(x + 2) = 0[/tex]

Solve for x

x = 1, -1 or -2

The above means that the graph passes through the points (-1,0), (-2,0) and (1,0)

See attachment for the graph of the function

Read more about graphs and functions at:

https://brainly.com/question/4025726