Answer:
It will be 5 seconds before the ball hits the ground
Step-by-step explanation:
∵ A ball is thrown from the top row of seats in a stadium
∵ The function
∵ h(t) = −16t² + 64t + 80
, gives the height, in feet, of the ball t seconds
after it is thrown
∵ The ball hits the ground
→ That means h(t) = 0
∵ h(t) = 0
∴ 0 = -16t² + 64t + 80
→ Reverse the two sides
∴ -16t² + 64t + 80 = 0
→ Divide both sides by -16 to simplify it
∵ [tex]\frac{-16t^{2}}{-16}+\frac{64t}{-16}+\frac{80}{-16}=\frac{0}{-16}[/tex]
∴ t² - 4t - 5 = 0
→ Factorize it into two factors
∵ t² = t × t
∵ -5 = -5 × 1
∵ -5t + 1t = -4t ⇒ the middle term
→ The factors are (t - 5) and (t + 1)
∴ (t - 5)(t + 1) = 0
→ Equate each factor by 0 to find t
∵ t - 5 = 0
→ Add 5 to both sides
∴ t = 5
∵ t + 1 = 0
→ Subtract 1 from both sides
∴ t = -1 ⇒ rejected because no negative value for the time
∵ t = 5
∴ It will be 5 seconds before the ball hits the ground
