91Ó°ÊÓ

Solve each equation. For equations with real solutions, support your answers graphically. $$4 x^{2}-20 x+25=0$$

Find the equation of the quadratic function satisfying the given conditions. (Hint: Determine values of \(a\), \(h,\) and \(k\) that satisfy \(P(x)=a(x-h)^{2}+k .\) ) Express your answer in the form \(P(x)=a x^{2}+b x+c .\) Use your calculator to support your results. Vertex \((-1,-4) ;\) through \((5,104)\)

For each polynomial function, (a) list all possible rational zeros, (b) use a graph to eliminate some of the possible zeros listed in part (a), (c) find all rational zeros, and (d) factor \(P(x)\). $$P(x)=x^{3}+6 x^{2}-x-30$$

RELATING CONCEPTS For individual or group investigation (Exercises \(55-60\) ) The close relationships among \(x\) -intercepts of a graph of a function, real zeros of the function, and real solutions of the associated equation should, by now, be apparent to you. Consider the graph of the polynomial function \(P(x)=x^{3}-2 x^{2}-11 x+12,\). What are the linear factors of \(P(x) ?\)

RELATING CONCEPTS For individual or group investigation (Exercises \(55-60\) ) The close relationships among \(x\) -intercepts of a graph of a function, real zeros of the function, and real solutions of the associated equation should, by now, be apparent to you. Consider the graph of the polynomial function \(P(x)=x^{3}-2 x^{2}-11 x+12,\). What are the solutions of the equation \(P(x)=0 ?\)

For each polynomial function, (a) list all possible rational zeros, (b) use a graph to eliminate some of the possible zeros listed in part (a), (c) find all rational zeros, and (d) factor \(P(x)\). $$P(x)=x^{3}-x^{2}-10 x-8$$

Multiply as indicated. Write each product in standard form. $$(-2+3 i)(4-2 i)$$

Find the equation of the quadratic function satisfying the given conditions. (Hint: Determine values of \(a\), \(h,\) and \(k\) that satisfy \(P(x)=a(x-h)^{2}+k .\) ) Express your answer in the form \(P(x)=a x^{2}+b x+c .\) Use your calculator to support your results. Vertex \((-2,-3) ;\) through \((0,-19)\)

Solve each equation. For equations with real solutions, support your answers graphically. $$9 x^{2}+12 x+4=0$$

Find all \(n\) complex solutions of each equation of the form \(x^{n}=k\) $$x^{2}=-4$$