Question

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

Answer 1

Answer:

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:

$y= -0.18(x-6)(x+6)\\y=-0.18(x^{2}-36)\\y=-0.18x^{2}+6.48x$

The equation is of a parabolic arch.

The general equation of a parabolic arch is:

$y=ax^{2}+bx+c$

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:

$x=-\frac{b}{2a}$

⇒

$x=-\frac{6.48}{2\times (-0.18)}\\\\x=18$

Compute the value of y as follows:

$y=-0.18x+6.48$

  $=(-0.18\times 18)+6.48\\=3.24\\\approx 3$

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