a dolphin jumps out of the water. the quadratic function y=-16x^2+32x models the dolphin's height above the water after x seconds.

Question

i have to solve the equation step by step i just don't know how ?

 

 

 

 

a dolphin jumps out of the water. the quadratic function y=-16x^2+32x models the dolphin's height above the water after x seconds. how long is the dolphin out of the water? what is the maximum height of the dolphin's jump?

Answer 1

y = f(x) ...

y equates to the height above the water

which is actually a function of time x

 

-16x² + 32x is the equation of a parabola

which, since the coefficient of the square term

is negative, opens downward.  The maximum

point for height y, will be at the vertex of the

parabola.

 

For y = ax²+bx+c...

the x coordinate of the vertex is at -b/2a

 

For y = -16x²+32x ...  a = -16, b = 32, c=0

 

-b/2a = -32/2(-16) = -32/-32 = 1

 

The maximum height is at the y coordinate of the vertex

so we need to find f(1)

 

f(1) = -16(1)² + 32(1) = -16 + 32 = 16

 

Our maximum height is 16 achieved at a time of 1 second

 

For the total time out of water we need to find the

x-intercepts...  The points where y=0

 

-16x² + 32x = 0

16x(-x + 2) = 0

Our 2 x-intercepts where the heigh will be zero are

at the points where x=0, and x=2

 

The total time out of water is 2 seconds.