Question

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

Answer 1

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