Final answer:
Using the quadratic formula, it's determined that the ball took 1 second to reach the target when solving the quadratic equation 0 = -16t² + 32t - 16.
Step-by-step explanation:
To find the time t it took for the ball to reach the target using the quadratic equation 0 = -16t² + 32t - 16, we will apply the quadratic formula. The quadratic formula is given by t = (-b ± sqrt(b² - 4ac))/(2a), where a, b, and c are coefficients from the quadratic equation at² + bt + c = 0. In this case, a = -16, b = 32, and c = -16.
Rearranging our equation to match the standard form, we have -16t² + 32t - 16 = 0. Plugging the values of a, b, and c into the quadratic formula, we get:
t = (-32 ± sqrt(32² - 4*(-16)*(-16)))/(2*(-16))
t = (-32 ± sqrt(1024 - 1024))/(-32)
t = (-32 ± 0)/(-32)
This simplifies to just t = 1 second. So, the ball took 1 second to reach the target.