91Ó°ÊÓ

Solve each equation using the quadratic formula. Simplify solutions, if possible. $$x^{2}+6 x+13=0$$

Solve polynomial inequality and graph the solution set on a real number line. \(6 x^{2}+x>1\)

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-x^{2}-2 x+8$$

Solve each equation using the quadratic formula. Simplify solutions, if possible. $$3 x^{2}=8 x-7$$

Solve each equation by making an appropriate substitution. If at any point in the solution process both sides of an equation are raised to an even power, a check is required. $$\left(x^{2}-1\right)^{2}-\left(x^{2}-1\right)=2$$

Solve polynomial inequality and graph the solution set on a real number line. \(4 x^{2}+7 x<-3\)

Solve each equation by the square root property. If possible, simplify radicals or rationalize denominators. Express imaginary solutions in the form \(a+b i .\) $$2(x+2)^{2}=16$$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-2 x^{2}+8 x-1$$

Solve each equation by making an appropriate substitution. If at any point in the solution process both sides of an equation are raised to an even power, a check is required. $$\left(x^{2}-2\right)^{2}-\left(x^{2}-2\right)=6$$

Solve each equation by the square root property. If possible, simplify radicals or rationalize denominators. Express imaginary solutions in the form \(a+b i .\) $$3(x+2)^{2}=36$$