91Ó°ÊÓ

Use the Intermediate Value Theorem to show that the function has at least one zero in the interval \([a, b] .\) (You do not have to approximate the zero.) $$f(x)=-x^{3}+2 x^{2}+7 x-3, \quad[3,4]$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=-\left(x^{2}+2 x-3\right)$$

Perform the indicated operation and write the result in standard form. $$(3+4 i)^{2}+(3-4 i)^{2}$$

Compare the graph of \(f(x)=8 / x^{3}\) with the graph of \(g\). $$g(x)=f(x)+5=\frac{8}{x^{3}}+5$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=5 x^{3}-9 x^{2}+28 x+6$$

Use the Intermediate Value Theorem to approximate the zero of \(f\) in the interval \([a, b]\). Give your approximation to the nearest tenth. (If you have a graphing utility, use it to help you approximate the zero.) $$f(x)=x^{3}+x-1, \quad[0,1]$$

Use synthetic division to divide. Divisor \(x-6\) Dividend $$10 x^{4}-50 x^{3}-800$$

Determine (a) the maximum number of turning points of the graph of the function and (b) the maximum number of real zeros of the function. $$f(x)=x^{2}-4 x+1$$

Use the Intermediate Value Theorem to approximate the zero of \(f\) in the interval \([a, b]\). Give your approximation to the nearest tenth. (If you have a graphing utility, use it to help you approximate the zero.) $$f(x)=x^{5}+x+1, \quad[-1,0]$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=-\left(x^{2}+6 x-3\right)$$