Quadratic Formula and Discriminant Quiz

Which of the options shows the quadratic formula?

• $x=\frac{b\pm\sqrt{b^2-4ac}}{2a}$

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{a}$

• $x=-b\frac{\pm\sqrt{b^2-4ac}}{2a}$

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Solve by using the quadratic formula: $4x^2-2x=12$  

•  $5,\ -\frac{15}{2}$  

•  $\frac{-5\pm5\sqrt{13}}{2}$  

•  $2,\ -\frac{3}{2}$  

•  $\frac{15}{2},\ -5$  

Solve by using the quadratic formula: $6x^2-10=11x$  

•  $\frac{2}{3},\ -\frac{5}{2}$  

•  $\frac{23}{3},\ -6$  

•  $\frac{-11\pm\sqrt{161}}{2}$  

•  $\frac{5}{2},\ -\frac{2}{3}$  

Solve by using the quadratic formula: $-5x^2=12+3x$  

•  $\frac{-3\pm i\sqrt{51}}{10}$  

•  $\frac{-3\pm i\sqrt{231}}{10}$  

•  $\frac{7\pm\sqrt{65}}{2}$  

•  $\frac{-7\pm i\sqrt{31}}{10}$  

Solve by using the quadratic formula: $7x^2-9=-7x$  

•  $-8,\ 10$  

•  $\frac{-7\pm4\sqrt{7}}{14}$  

•  $\frac{-7\pm i\sqrt{479}}{22}$  

•  $\frac{-7\pm\sqrt{301}}{14}$  

Solve by using the quadratic formula: $x^2-60=-7x$  

•  $5,\ -12$  

•  $5,\ -10$  

•  $\frac{10}{3},\ -5$  

•  $\frac{5\pm5i\sqrt{23}}{6}$  

Solve by using the quadratic formula: $-8x^2=4x-19$  

•  $2,\ -\frac{3}{2}$  

•  $\pm\frac{\sqrt{66}}{6}$  

•  $\frac{-1\pm\sqrt{39}}{4}$  

•  $\frac{-1\pm\sqrt{15}}{2}$  

Solve by using the quadratic formula: $x^2=-15-10x$  

•  $\frac{-1\pm i\sqrt{95}}{16}$  

•  $-5\pm\sqrt{10}$  

•  $5\pm\sqrt{10}$  

•  $\frac{1\pm i\sqrt{95}}{16}$  

Solve by using the quadratic formula: $11x^2+7x=-8$  

•  $\frac{-2\pm2\sqrt{11}}{5}$  

•  $\frac{7\pm\sqrt{401}}{22}$  

•  $\frac{4\pm i\sqrt{83}}{11}$  

•  $\frac{-7\pm i\sqrt{303}}{22}$  

A golf ball is hit with an initial velocity of 64 ft/s. The function $h\left(t\right)=-16t^2+64t$   models the height h (in feet) of the golf ball at time t (in seconds). Does the golf ball reach a height of 60 feet?

Choose the most appropriate answer.

• Yes because the equation has two real solutions for t

• Yes because 60 is a positive number

• No because the equation has two non-real solutions for t

• No because 60 feet is an unrealistic height