How many seconds will it take for the birdie to hit the ground?

Question

The height of h (in feet) of a badminton birdie t seconds after it is hit can be modeled by the function h=-16t^2+32t+4. How long does the birdie take to hit the ground? Round your answer to the nearest hundredth. About _ seconds

Answer 1

Hi Robin, let see if we can work through this. It may help to draw a picture of the curve. We know it is “hit” and then hits the ground, so it will be a downward facing curve or parabola or quadratic function. It is hit when t = 0 (not relevant to solution, only for graphing purposes)

we are looking for the time t when it hits the ground, so we know that the height, h=0 at the ground.

solve 0= -16t² + 32t + 4, where t is the time in seconds

we can first factor out -4, a common factor in all three places.

0 = -4(4t² - 8t - 1)

*Always keep track of your negatives and positives

you should be able to multiply it back and get your original equation

then we can try to factor the polynomial normally:

0 = -4 (4t - __)(t + __)

we find that no combination can factor equally. We must use the quadratic formula:

x = (-b + or - (b² - 4ac)^1/2) x = t

2a

(I used the 1/2 exponent which is the same as the square root)

where 0 = ax² + bx + c *pay close attention to the positive and negative signs here.

you can plug the a, b, and c from the equation into the formula and get your value. The positive answer is the solution in seconds. The “negative” answer would be there it would hit the ground if you completed the parabola before the birdie was it (back in time).

to check your solution, put it back into the original equation and you should get zero (0), where the birdie hits the ground.

please message me if you have any more questions or want to set up some lessons online! I’d love to help more!