Challenge A baseball player hits a baseball and its height is modeled by the function h (t) = - 16t^2=12t+4. If t represents time, in seconds, find the time in seconds when the ball hit the ground

That is when height or h (t) = 0

0=-16t^2+12t+4

use math to solve

I will complete the square

group t terms

0 = (-16t^2+12t) + 4

factor out quadratic coefient

0=-16 (t^2 - (3/4) t) + 4

take 1/2 of linear coefient and squaer it

(-3/4) / 2=-3/8, (-3/8) ^2=9/64

take negative and positive of it and add to inside of parenthasees

0=-16 (t^2 + (-3/4) t+9/64-9/64) + 4

factor pefect square

0=-16 ((t-3/8) ^2-9/64) + 4

expand/distribute

0=-16 (t-3/8) ^2+9/4+4

0=-16 (t-3/8) ^2+25/4

add - 16 (t-3/8) ^2 to both sides

16 (t-3/8) ^2=25/4

divide both sides by 16

(t-3/8) ^2=25/64

sqrt both sides

remmber positive and negative roots

t-3/8=+/-5/8

add 3/8 to both sides

t=3/8+/-5/8

t=3/8+5/8 or t=3/8-5/8

t=8/8 or t=-2/8

t=1 or - 1/4

we can't have negative time so

at t=1

1 second