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.
