Ahovercraft takes off from a platform. its height (in meters), x seconds after takeoff, is modeled by: h(x)=-2x^2+20x+48h. what is the maximum height that the hovercraft will reach?

Given function for height is h(x)= -2x^2+20x+48, where x is the number of seconds after takeoff hovercraft.

We need to find the maximum height of the hovercraft.

The given function is a quadratic function.

And a quadratic function represents a parabola.

The maximum height of the parabola is the vertex point.

So, we need to find the y-coordinate of the vertex to find the maximum height of hovercraft.

We know formula for x-coordinate of vertex is given by

x = -b/2a

For the given function a=-2 and b=20.

Plugging values of a and b in above formula, we get

x=-20/2(-2) = -20/-4 = 5.

We got x-coordinate of the vertex point = 5.

Plugging x=5 in given function of height, we get

h(5) = -2(5)^2+20(5)+48

=-2(25) +100 +48

=-50+100+48

=50+48

=98.

y=98

Therefore, the maximum height of the hovercraft will reach = 98 meters.

a

step-by-step explanation:

a