91Ó°ÊÓ

Find the equation of the line that contains the point (2,3) and that is parallel to the line containing the points (7,1) and (5,6) .

For Exercises 27-32, suppose $$ r(x)=\frac{x+1}{x^{2}+3} \quad \text { and } \quad s(x)=\frac{x+2}{x^{2}+5} $$ What is the range of \(r ?\)

Find all choices of \(b, c,\) and \(d\) such that -3 and 2 are the only zeros of the polynomial \(p\) defined by $$ p(x)=x^{3}+b x^{2}+c x+d $$

Find the equation of the line that contains the point (-4,3) and that is parallel to the line containing the points (3,-7) and (6,-9)

Simplify the given expression. $$ \left(\frac{\left(x^{-3} y^{5}\right)^{-4}}{\left(x^{-5} y^{-2}\right)^{-3}}\right)^{-2} $$

For Exercises \(31-34,\) for the given function \(f:\) (a) Write \(f(x)\) in the form \(a(x-h)^{2}+k\). (b) Find the value of \(x\) where \(f(x)\) attains its minimum value or its maximum value. (c) Sketch the graph of \(f\) on an interval of length 2 centered at the mumber where \(f\) attains its minimum or maximum value. (d) Find the vertex of the graph of \(f\). $$ f(x)=-2 x^{2}+5 x-2 $$

Give an example of two polynomials of degree 4 whose sum has degree 3 .

Find a number \(t\) such that the line containing the points \((t, 2)\) and (3,5) is parallel to the line containing the points (-1,4) and (-3,-2)

Find a formula for \(f\) o \(g\) given the indicated functions \(f\) and \(g\). $$ f(x)=x^{2}, g(x)=x^{3} $$

For Exercises \(31-34,\) for the given function \(f:\) (a) Write \(f(x)\) in the form \(a(x-h)^{2}+k\). (b) Find the value of \(x\) where \(f(x)\) attains its minimum value or its maximum value. (c) Sketch the graph of \(f\) on an interval of length 2 centered at the mumber where \(f\) attains its minimum or maximum value. (d) Find the vertex of the graph of \(f\). $$ f(x)=-3 x^{2}+5 x-1 $$