91Ó°ÊÓ

Describe the graph of the function and identify the vertex. $$f(x)=-x^{2}+x+6$$

Use a graphing utility to graph the function and determine any \(x\) -intercepts. Set \(y=0\) and solve the resulting equation to confirm your result. $$y=x+2-\frac{1}{x+1}$$

Find a polynomial function with the given zeros, multiplicities, and degree. (There are many correct answers.) Zero: \(-4,\) multiplicity: 2 Zero: \(3,\) multiplicity: 2 Degree: 4

Describe the graph of the function and identify the vertex. $$f(x)=6 x^{2}+5 x-6$$

Let z-represent a positive real number. Describe how the family of parabolas represented by the given function compares with the graph of \(g(x)=x^{2}\) \(f(x)=(x-z)^{2}\)

Find the rational zeros of the polynomial function. $$P(x)=x^{4}-\frac{25}{4} x^{2}+9=\frac{1}{4}\left(4 x^{4}-25 x^{2}+36\right)$$

Use a graphing utility to graph the function and determine any \(x\) -intercepts. Set \(y=0\) and solve the resulting equation to confirm your result. $$y=2 x-1+\frac{1}{x-2}$$

Let z-represent a positive real number. Describe how the family of parabolas represented by the given function compares with the graph of \(g(x)=x^{2}\) \(f(x)=x^{2}-z\)

Find the rational zeros of the polynomial function. $$f(x)=x^{3}-\frac{3}{2} x^{2}-\frac{23}{2} x+6=\frac{1}{2}\left(2 x^{3}-3 x^{2}-23 x+12\right)$$

Describe the graph of the function and identify the vertex. $$f(x)=4 x^{2}+2 x-12$$