Question

The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modelled by the function h = -5t2 + 15t + 20 What was the maximum height of the flare?

Answer 1

31.25 metres at t=1.5 seconds.

Explanation:

The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function

`h=-5t^2+15t+20`

We need to find the maximum height of the flare.

In the given quadratic function, the leading coefficient is negative it means the function represents the downward parabola.

Vertex of a downward parabola is the point of maxima.

If a quadratic function is
`f(x)=ax^2+bx+c`, then

`Vertex=\left(-(b)/(2a), f(-(b)/(2a))\right)`

In the given function, a=-5, b=15, c=20. So,

`-(b)/(2a)=-(15)/(2(-5))=(15)/(10)=1.5`

Put x=1.5 in the given function.

`h=-5(1.5)^2+15(1.5)+20`

`h=31.25`

Therefore, the maximum height of the flare is 31.25 metres and t=1.5 seconds.