Question

the quadratic model $f(x) = -5x^2 + 200$ represents the approximate height, in meters, of a ball $x$ seconds after being dropped. the ball is 50 meters from the ground after about how many seconds?
2.45
3.16
5.48
7.07

Explanation:

Step1: Set height to 50 meters

$50 = -5x^2 + 200$

Step2: Rearrange to isolate $x^2$

$-5x^2 = 50 - 200$
$-5x^2 = -150$
$x^2 = \frac{-150}{-5} = 30$

Step3: Solve for positive $x$

$x = \sqrt{30} \approx 5.48$

Answer:

5.48 (Option C)