Answer: The ball will hit the ground 5 seconds after being thrown.
Step-by-step explanation:
The correct function is: [tex]h (t) =-16t^2 +64t+80[/tex]
You can rewrite the Quadratic function given in the exercise with making [tex]h(t)=0[/tex]. Then this is:
[tex]0=-16t^2 +64t+80[/tex]
Now you can simplify the equation dividing both sides by -16. So you get:
[tex]\frac{0}{-16}=\frac{-16t^2 +64t+80}{-16}\\\\0=t^2-4t-5[/tex]
To find the solution of the Quadratic equation, you can facfor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.
Therefore, you get this result:
[tex]0=(t-5)(t+1)\\\\t_1=5\\t_2=-1[/tex]
Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.
