A rock is thrown upward from the top of a 112-foot high cliff overlooking the ocean at a speed of 96 feet per second. The rock's helght above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . What is the maximum height in feet, that the rock will reach? Do not include units in your answer

256 feet

Step-by-step explanation:

To find the maximum height, we have to find the vertex of the parabola, which is formed by the situation.

First, find the axis of symmetry using -(b/2a). This will give us the x value of the vertex.

Plug in b into the equation:

-(b/2a)

-(96 / 2(-16))

-(96 / -32)

-(-3)

= 3

Now, plug in 3 as x into the given equation, to find the maximum height that the rock will reach:

H(t) = -16t² + 96t + 112

H(3) = -16(3²) + 96(3) + 112

H(3) = 256

So, the maximum height that the rock will reach is 256 feet

yes

step-by-step explanation:

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.