Arock is thrown upward from a bridge into a river below. the function f ( t ) = − 16 t 2 + 43 t + 114 f(t)=-16t2+43t+114 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t t since the rock was thrown.
a. what is the bridge's height above the water?
b. how many seconds after being thrown does the rock hit the water?
c. how many seconds after being thrown does the rock reach its maximum height above the water?
d. what is the rock's maximum height above the water?

(a) The bridge's height above the water is 114 feet.

(b) After 4.332 seconds the rock hit the water.

(c) After 1.34375 seconds the rock reach its maximum height above the water.

(d) The rock's maximum height above the water is 142.89 feet.

Step-by-step explanation:

The given function is

(a)

At t=0

Therefore, the bridge's height above the water is 114 feet.

(b)

If a quadratic equation is defined as , then the quadratic formula is

In the given function a=-16, b=43 and c=114.

Time can not be negative. It means, at t=4.332 the rock hit the water.

Therefore, after 4.332 seconds the rock hit the water.

(c)

The vertex of quadratic function is

For the given function a=-16, b=43 and c=114.

The leading coefficient is negative. It means the vertex is point of maxima.

Therefore, after 1.34375 seconds the rock reach its maximum height above the water.

(d)

Substitute t=1.34375 in the given function.

Therefore, the rock's maximum height above the water is 142.89 feet.

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2