91Ó°ÊÓ

Solve each quadratic equation by extraction of roots. $$ 3 a^{2}-18=0 $$

For the following problems, write the values of \(a, b,\) and \(c\) in quadratic equations. $$ -3 a^{2}+4 a-1=0 $$

If an object is thrown vertically upward, its height \(h,\) above the ground, in feet, after \(t\) seconds is given by \(h=h_{0}+v_{0} t-16 t^{2},\) where \(h_{0}\) is the initial height from which the object is thrown and \(v_{0}\) is the initial velocity of the object. Using this formula and an approach like that of Sample Set \(A\), solve this problem. A ball thrown vertically into the air has the equation of motion \(h=48+32 t-16 t^{2}\). (a) How high is the ball at \(t=0\) (the initial height of the ball)? (b) How high is the ball at \(t=1\) (after 1 second in the air)? (c) When does the ball hit the ground? (Hint: Determine the appropriate value for \(h\) then solve for \(t .)\)

For the following problems, solve the equations. $$ 6 r^{2}-36=0 $$

For the following problems, solve the equations, if possible. $$ (x-4)(x+2)=0 $$

For the following problems, solve each of the quadratic equations using the method of extraction of roots. $$ x^{2}=49 $$

For the following problems, solve the equations by completing the square. $$ x^{2}+4 x+4=0 $$

For the following problems, solve the equations. $$ a^{2}+6 a+8=0 $$

Solve each quadratic equation by extraction of roots. $$ (x-5)^{2}=1 $$

For the following problems, solve each of the quadratic equations using the method of extraction of roots. $$ a^{2}=9 $$