Afrog leaps 2 feet. the highest point in the jump is 6 inches. assume the frog starts at (0,0). what quadratic function models the path of the jump? specifty the units you use.

1 feet =12 inche
0.5 feet=6 inches
range =2 feet
maximum height =0.5 feet
range = inital velocity *t
vf=vi+at
f(t)=at^2+bt+c
we have the point (0,0)
which means the object travelled 0 meters in 0 second
f(0)=c=0
so c=0
since we want our parobala to have it second root at 2
we have the point(2,0)
substituting
0=4a+2b
b=-2a
we also have the vertex (tmax,0.5)
we know that our
tmax=-b/2a
substituting b=-2a
tmax=--2a/2a=1
f(1)=0.5
0.5=a+b
we have our pervious equation
b=-2a
solving this system
0.5=-a
a=-0.5
and b=-2(-0.5)=1
our equation is f(x)=-0.5t^2+t