91Ó°ÊÓ

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$5 x^{2}=-2 x-3$$

For function of the form \(f(x)=\) \(a x^{2}+b x+c,\) find the discriminant, \(b^{2}-4 a c,\) and use it to determine the number of \(x\) -intercepts of the graph of \(f .\) Also determine the number of real solutions of the equation \(f(x)=0.\) $$f(x)=2 x^{2}+x+1$$

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$7 x^{2}=-x-1$$

Suppose \(f\) is constant on an interval \([a, b] .\) Show that the average rate of change of \(f\) on \([a, b]\) is zero.

Graph the function \(f(t)=t^{2}-4\) in a decimal window. Using your graph, determine the values of \(t\) for which \(f(t) \geq 0\).

In Exercises \(67-86,\) find expressions for \((f \circ g)(x)\) and \((g \circ f)(x)\) Give the domains of \(f \circ g\) and \(g \circ f\). $$f(x)=2 x+5 ; g(x)=3 x^{2}$$

For function of the form \(f(x)=\) \(a x^{2}+b x+c,\) find the discriminant, \(b^{2}-4 a c,\) and use it to determine the number of \(x\)-intercepts of the graph of \(f .\) Also determine the number of real solutions of the equation \(f(x)=0.\) $$f(x)=3 x^{2}-4 x+4$$

Find all solutions of the quadratic equation. Relate the solutions of the equation to the zeros of an appropriate quadratic function. $$-3 x^{2}+8 x=16$$

If the average rate of change of a function on an interval is zero, docs that mean the function is constant on that interval?

Use a graphing utility to solve the problem. Graph \(f(x)=|x+3.5|\) and \(g(x)=|x|+3.5 .\) Describe each graph in terms of transformations of the graph of \(h(x)=|x|\).