Wrestler Big Body McRoid flips his opponent Wee Willy Stinky

Wrestler Big Body McRoid flips his opponent Wee Willy Stinkyflesh and Wee Willy\'s path is described by the equation h(x) = - 4x^2 + 6x + 7, where x is time in seconds and h(x) is height measured in feet. Determine the height from which Wee Willy was thrown. Determine the maximum height Wee Willy obtained (Round to the hundredths place). Determine how much time had passed when Wee Willy was at his maximum height. (Round to the hundredths place). Determine how much time had passed when Wee Willy fell to the ground. (Round to the hundredths place). At what time was Wee Willy at 3 feet in the air?

Solution

h(x) = -4x^2 +6x +7

a) when Wee willy was thrown i.e time =0 x =0

So, h(0) = 7 feet

b) maximum height:

find the vertex of quadraticev function ax^2 +bx +c

x = -b/2a

So, x = -6/(2*-4) = 6/8 = 3/4 =0.75 sec

Max. height h(0.75) = -4(0.75)^2 + 6*0.75 +7 = 9.25 feet

c) time at max. height = 0.75sec

d) When he fell to the ground h(x) =0

-4x^2 +6x +7 =0

solve the quadratice for x: x = -0.77 , 2.27

Neglect -ve valueas tiome cannot be a -ve qty

So, x = 2.27 sec

e) h(x) =3 feet

3 = -4x^2 +6x +7

solve the quadratic for x x = -0.5 , 2

Neglect -ve valueas tiome cannot be a -ve qty

So,. x = 2sec