Use a graphing calculator to examine the graphs of the following functions a.f(x)=\frac{1}{2}x^{2}+2x\ b.f(x)=x(x+1)^{2}(x-1)^{2}\ c.f(x)=x^{3}-x^{2}+31x+40

Anonym 2021-08-07 Answered
Use a graphing calculator to examine the graphs of the following functions. Determine ⋅⋅ the degree of the polynomial ⋅⋅ the leading coefficient ⋅⋅ the end behavior of the polynomial function ⋅⋅ the maximum number of zeros ⋅⋅ the maximum number of turning points (relative maxima and minima) a.f(x)=12x2+2x b.f(x)=x(x+1)2(x1)2 c.f(x)=x3x2+31x+40
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un4t5o4v
Answered 2021-08-08 Author has 105 answers

Step 1
a.Degree:2(highest-degree monomial is 12x2).
Leading coefficient: 12(coefficient of highest-degree monomial)
End behavior: y as x± (even-degree polynomial with positive leading coefficient)
Maximum number of zeros: 2(same as degree)
Maximum number of turning points: 1(one less than degree)
image

Step 2
b. Degree:5(product of 5 linear factors)
Leading coefficient: 1(product of coefficient of x terms)
End behavior: y  as x.y as  (odd-degree polynomial with positive leading coefficient)
Maximum number of zeros: 5(same as degree)
Maximum number of turning points: 4 (one less than degree)
image Step 3
c. Degree: 3 (degree of highest-degree monomial x3)
Leading coefficient: 1(coefficient of highest-degree monomial)
End behavior: y as x.y as x (odd-degree polynomial with positive leading coefficient)
Maximum number of zeros: 3 (same as degree)
Maximum number of turning points: 2 (one less than degree)
image

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