Students are having a gum spitting contest and one student o

Students are having a gum spitting contest, and one student observes the gum follow a parabolic curve according to the equation -16x^2 +48x+4. What is the highest point the gum wad reaches and after how much time?
After how many seconds will the gum wad hit the ground?

Solution

equation h(x)= -16x^2 +48x+4. What is the highest point the gum wad reaches and after how much time?
High point at x=-b/2a=-48/(-32)=3/2
h(3/2)=-16(3/2)^2+48(3/2)+4
h(3/2)=-16(9/4)+72+4
h(3/2)=-36+76=40
The highest point is 40 ft.; the time is 1.5 seconds
-------------------
After how many seconds will the gum wad hit the ground?
When it hits the ground the height will be zero.
-16x^2+48x+4=0
Divide thru by 4 to get:
-4x^2+12x+1=0
x=[-12+-sqrt(144-4*-4**1]/-8
x=[-12+-sqrt160]/-8
x=[-12+4sqrt10]/-8 or x=[-12-4sqrt10]/-8
x=negative or x=[-24.649...]/-8=3.08 seconds