91Ó°ÊÓ

Use a graphing utility to graph the quadratic function and find the \(x\) -intercepts of the graph. Then find the \(x\) -intercepts algebraically to verify your answer. \(y=-\frac{1}{2}\left(x^{2}-6 x-7\right)\)

A real zero of the numerator of a rational function \(f\) is \(x=c .\) Must \(x=c\) also be a zero of \(f ?\) Explain.

Find all the real zeros of the polynomial function. Determine the multiplicity of each zero. Use a graphing utility to verify your results. \(f(x)=x^{2}+x-2\)

Sketch the graph of the rational function by hand. As sketching aids, check for intercepts, vertical asymptotes, and slant asymptotes. $$f(x)=\frac{x^{3}}{x^{2}+4}$$

A polynomial function \(f\) with real coefficients has the given degree, zeros, and solution point. Write the function (a) in completely factored form and (b) in polynomial form. Degree 3 Zeros $$-2,2+2 \sqrt{2} i$$ Solution Point $$f(-1)=-34$$

Use a graphing utility to graph the quadratic function and find the \(x\) -intercepts of the graph. Then find the \(x\) -intercepts algebraically to verify your answer. \(y=\frac{7}{10}\left(x^{2}+12 x-45\right)\)

Find all the real zeros of the polynomial function. Determine the multiplicity of each zero. Use a graphing utility to verify your results. \(f(x)=2 x^{2}-14 x+24\)

When the graph of a rational function \(f\) has a vertical asymptote at \(x=4,\) can \(f\) have a common factor of \((x-4)\) in the numerator and denominator? Explain.

Find all the real zeros of the polynomial function. Determine the multiplicity of each zero. Use a graphing utility to verify your results. \(f(t)=t^{3}-4 t^{2}+4 t\)

Sketch the graph of the rational function by hand. As sketching aids, check for intercepts, vertical asymptotes, and slant asymptotes. $$f(x)=\frac{x^{3}+2 x^{2}+4}{2 x^{2}+1}$$