Question

A hovercraft takes off from a platform. Its height (in meters), xxx seconds after takeoff, is modeled by: h(x)=-2x^2+20x+48h(x)=−2x 2 +20x+48h, left parenthesis, x, right parenthesis, equals, minus, 2, x, start superscript, 2, end superscript, plus, 20, x, plus, 48 what is the maximum height that the hovercraft will reach?

Answer 1

the maximum height is the y-value of the vertex.

h(x) = -2x² + 20x + 48

       a=-2, b=20, c=48

$x = \frac{-b}{2a} = \frac{-20}{2(-2)} = \frac{-20}{-4} = 5$

h(5) = -2(5)² + 20(5) + 48

      =  -50   +  100   + 48

      =          50         + 48

      =                98

Answer: 98 meters