91Ó°ÊÓ

Write an equation for a function having a graph with the same shape as the graph of \(f(x)=\frac{3}{5} x^{2},\) but with the given point as the vertex. $$ (9,-6) $$

Solve by completing the square. Remember to first. divide, as in Example \(10,\) so that the coefficient of \(x^{2}\) is 1 $$ 2 x^{2}-5 x-3=0 $$

Use a graphing calculator to graph each function and find solutions of \(f(x)=0 .\) Then solve the inequalities \(f(x)<0\) and \(f(x)>0\). $$f(x)=x+\frac{1}{x}$$

For each equation under the given condition, (a) find \(k\) and (b) find the other solution. \(k x^{2}-2 x+k=0 ;\) one solution is \(-3\)

Use a graphing calculator to solve $$x^{4}-x^{3}-13 x^{2}+x+12=0$$

One solution of \(k x^{2}+3 x-k=0\) is \(-2 .\) Find the other.

For each equation under the given condition, (a) find \(k\) and (b) find the other solution. \(x^{2}-k x+2=0 ;\) one solution is \(1+i\)

Use a graphing calculator to graph each function and find solutions of \(f(x)=0 .\) Then solve the inequalities \(f(x)<0\) and \(f(x)>0\). $$f(x)=x-\sqrt{x}, x \geq 0$$

Write an equation for a function having a graph with the same shape as the graph of \(f(x)=\frac{3}{5} x^{2},\) but with the given point as the vertex. $$ (-4,-2) $$

Solve by completing the square. Remember to first. divide, as in Example \(10,\) so that the coefficient of \(x^{2}\) is 1. Find the \(x\) -intercepts of the graph of \(f(x)=4 x^{2}+2 x-3\)