Question

What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?

Answer 1

The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?

The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.

Generally, the equation for is zeros  mathematically given as

y=x^4−2x^3−11x^2+12x+36

Therefore

(x+2)^2(x-3)^2=0

x=-2

x=3

since the graph attached has a positive leading coefficient and a positive degree

In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

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