91Ó°ÊÓ

In \(9-26,\) solve each quadratic equation by completing the square. Express the answer in simplest radical form. $$ 2 x^{2}-6 x+3=0 $$

The height, in feet, to which of a golf ball rises when shot upward from ground level is described by the function h(t) \(=-16 t^{2}+48 t\) where \(t\) is the time elapsed in seconds. Use the discriminant to determine if the golf ball will reach a height of 32 feet.

In \(18-35,\) find each common solution algebraically. Express irrational roots in simplest radical form. $$ \begin{array}{l}{2 x^{2}+x-y+1=0} \\ {x-y+7=0}\end{array} $$

Write a quadratic equation with integer coefficients for each pair of roots. \(2,5\)

Write a quadratic equation with integer coefficients for each pair of roots. \(4,7\)

In \(19-34,\) write each sum or difference in terms of \(i\) $$ -\frac{1}{2}+\sqrt{-\frac{2}{3}}-\frac{1}{2}+\sqrt{-\frac{24}{9}} $$

Write a quadratic equation with integer coefficients for each pair of roots. \(-2,-1\)

In \(28-33,\) without graphing the parabola, describe the translation, reflection, and \(/\) or scaling that must be applied to \(y=x^{2}\) to obtain the graph of each given function. $$ f(x)=3 x^{2}+6 x+3 $$

Write a quadratic equation with integer coefficients for each pair of roots. \(\frac{3}{2} i,-\frac{3}{2} i\)

The perimeter of a rectangle is 24 feet. The area of the rectangle is 32 square feet. Find the dimensions of the rectangle.