A dome tent’s arch is modeled by y= -0.18(x-6)(x+6)where x and y are measured in feet.

The height of the highest point of the arch is 3 feet.

Step-by-step explanation:

The complete question is:

A dome tent’s arch is modeled by y= -0.18(x-6)(x+6) where x and y are measured in feet. To the nearest foot, what is the height of the highest point of the arch.

Solution:

The expression provided is:

The equation is of a parabolic arch.

The general equation of a parabolic arch is:

So,

a = -0.18

b = 6.48

c = 0

Highest point of the parabolic arch is the vertex of the parabolic equation if a < 0 .

As a = -0.18 < 0, the ordinate of vertex of equation will give the height of highest point of arch.

For a parabola the abscissa of vertex is given as follows:

⇒

Compute the value of y as follows:

Thus, the height of the highest point of the arch is 3 feet.