Maths- Polynomials

Question

A stone is tossed from a point W into the air. The height Y metres of the stone above ground level at time t seconds is given by y=-t²+4t+5. 

                (a) How far is W from the ground level?

                (b) If -t²+4t+5 can be expressed as -(t-2)² +P, find the value of P.

                (c) Hence, deduce the maximum vertical distance of the stone above the point W and the time taken to reach thi distance.

Answer 1

a) At release, t = 0.

 

0 + 0 + 5 = 5 meters off the ground

 

b) -t² + 4t = -5

t² - 4t = 5

t² - 4t + 4 = 5 + 4

(t - 2)² = 9

-(t - 2)² = -9

-(t - 2)²  + 9 = 0

p = 9

 

c) t = -b/2a = -4/(2(-1)) = -4/-2 = 2 seconds

 

-2² + 4(2) + 5 = -4 + 8 + 5 = 9 meters

 

9 - 5 = 4 meters above point W