A) p(r) = 2r2 + 2r - 1
To make it easier to write, I am going to replace p(r) with y:
y = 2r2 + 2r - 1
Now, solve for r:
y + 1 = 2r2 + 2r
y + 1 = 2(r2 + r)
Complete the square:
y + 1 + ½ = 2(r2 + r + ¼)
y + 3/2 = 2(r2 + r + ¼)
(y + 3/2)/2 = (r + ½)2
Take the square root (using the positive portion):
√( y/2 + 3/4 ) = r + ½
r = -½ +√( y/2 + 3/4 )
r = -½ +√( p(r)/2 + 3/4 )
B) h(t) = - 4.9(t + 3)2 + 45.8
y = - 4.9(t + 3)2 + 45.8
y - 45.8 = - 4.9(t + 3)2
(y - 45.8) / -4.9 = (t + 3)2
√( (y - 45.8) / -4.9 ) = t + 3
t = -3 + √( (y - 45.8) / -4.9 )
t = -3 + √( (h(t) - 45.8) / -4.9 )
A) p(r) = 2r2 + 2r - 1
To make it easier to write, I am going to replace p(r) with y:
y = 2r2 + 2r - 1
Now, solve for r:
y + 1 = 2r2 + 2r
y + 1 = 2(r2 + r)
Complete the square:
y + 1 + ½ = 2(r2 + r + ¼)
y + 3/2 = 2(r2 + r + ¼)
(y + 3/2)/2 = (r + ½)2
Take the square root (using the positive portion):
√( y/2 + 3/4 ) = r + ½
r = -½ +√( y/2 + 3/4 )
r = -½ +√( p(r)/2 + 3/4 )
B) h(t) = - 4.9(t + 3)2 + 45.8
y = - 4.9(t + 3)2 + 45.8
y - 45.8 = - 4.9(t + 3)2
(y - 45.8) / -4.9 = (t + 3)2
√( (y - 45.8) / -4.9 ) = t + 3
t = -3 + √( (y - 45.8) / -4.9 )
t = -3 + √( (h(t) - 45.8) / -4.9 )