High School Math Help

Question

The height of two different projectiles after they are launched are modeled by f(x) and g(x). The function f(x) is defined as f(x)=-16x²+42+12. The tables contain the value for the quadratic function g(x). What is the approximate difference in the maximum heights achieved by the two projectiles? Express you answer to the nearest tenth. 

 

x        0        1        2

gx      9       33       25

Answer 1

f =-16x^2 +42x +12

f'= -32x+42=0

x= 21/16 seconds for max height

f(1)=38 ft

f(2)=32 ft

g(1)=33

g(2)=25

g= -16x^2 +40x +9

g'= -32x+40=0

x=5/4 seconds for max height

f >g by about 5.4 ft