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

Step 1
a.Degree:2(highest-degree monomial is ${\displaystyle \frac{1}{2}{x}^2}$).
Leading coefficient: ${\displaystyle \frac{1}{2}}$(coefficient of highest-degree monomial)
End behavior: ${\displaystyle y\to \mathrm{\infty }asx\to \pm \mathrm{\infty }}$ (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)

Step 2
b. Degree:5(product of 5 linear factors)
Leading coefficient: 1(product of coefficient of x terms)
End behavior: y $\to \mathrm{\infty }asx\to \mathrm{\infty }.y\to -\mathrm{\infty }as\to -\mathrm{\infty }$ (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)
Step 3
c. Degree: 3 (degree of highest-degree monomial ${\displaystyle x^3}$)
Leading coefficient: 1(coefficient of highest-degree monomial)
End behavior: $y\to \mathrm{\infty }asx\to \mathrm{\infty }.y\to -\mathrm{\infty }asx\to -\mathrm{\infty }$ (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)