Question

Jack shoots a rocket upward from the ground. the height of the rocket is modeled by (x-2)^2=25. the time after launch is represented by x.
a. how high will the rocket reach?
b. at what time will the rocket reach its highest point?
c. at what time will the rocket be back on the ground?​

Answer 1

Using a quadratic function, we have that:

a) The rocket reaches a maximum height of 25 units.

b) The rocket reaches it's highest point after 2 seconds.

c) The rocket will be back on the ground after 7 seconds.

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, placing it in vertex form, the equation for the height h is given by:

h = -(x - 2)² + 25.

Hence the vertex is (2,25), which means that:

a) The rocket reaches a maximum height of 25 units.

b) The rocket reaches it's highest point after 2 seconds.

The rocket hits the ground when h = 0, hence:

-(x - 2)² + 25 = 0

(x - 2)² = 25

Applying the square root to both sides:

x - 2 = 5.

x = 7.

The rocket will be back on the ground after 7 seconds.

More can be learned about quadratic functions at brainly.com/question/24737967

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