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Consider the graph of the sixth-degree polynomial function f.



Replace the values b, c, and d to write function f.
f(x)=(x-b)(x-c)^2(x-d)^3

Consider the graph of the sixthdegree polynomial function f Replace the values b c and d to write function f fxxbxc2xd3 class=

Respuesta :

Matthewgarnett0

Answer:

f(x)=(x-1)(x+1)^2(x-4)^3

Step-by-step explanation:

The zeros of the function are x=-1, x=1, and x=4, so its factors are x+1, x-1, and x-4.

The graph touches, but doesn’t cross, the x-axis at x=-1. So the factor x+1 is a repeated factor with an even multiplicity.

The graph crosses the x-axis at x=4, but with a little curve before and after it meets this point. So the factor x+4 is a repeated factor with odd multiplicity.

The graph crosses the x-axis at x=1 with no curve before or after. So the factor x-1 is not a repeated factor.

Therefore, function f is defined by f(x)=(x-1)(x+1)^2(x-4)^3.

The sixth-degree polynomial that shows in the graph is [tex]\rm f(x) = (x+1)(x-1)^2(x-4)^3[/tex] and this can be determined by evaluating the x-intercept of the given graph.

Given :

Sixth-degree polynomial -- [tex]\rm f(x) = (x-b)(x-c)^2(x-d)^3[/tex]

The following steps can be used in order to determine the value of b, c, and d:

Step 1 - Write the given sixth-degree polynomial.

[tex]\rm f(x) = (x-b)(x-c)^2(x-d)^3[/tex]

Step 2 - Observe the given graph and determine the x-intercept of the graph of the sixth-degree polynomial.

Step 3 - So, the x-intercepts that are the values of b, c, and d is given below:

b = -1

c = 1

d = 4

Step 4 - Substitute the values in the given sixth-degree polynomial.

[tex]\rm f(x) = (x+1)(x-1)^2(x-4)^3[/tex]

For more information, refer to the link given below:

https://brainly.com/question/14375099

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