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

Set $f(x)=50$, so:
$$50 = -5x^2 + 200$$

Step2: Rearrange to isolate $x^2$

Subtract 200 from both sides:
$$50 - 200 = -5x^2$$
$$-150 = -5x^2$$
Divide by -5:
$$x^2 = \frac{-150}{-5} = 30$$

Step3: Solve for positive $x$

Take square root (time is positive):
$$x = \sqrt{30} \approx 5.48$$

Answer:

5.48