Respuesta :
Answer:
31.25 metres at t=1.5 seconds.
Step-by-step 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
[tex]h=-5t^2+15t+20[/tex]
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 [tex]f(x)=ax^2+bx+c[/tex], then
[tex]Vertex=\left(-\dfrac{b}{2a}, f(-\dfrac{b}{2a})\right)[/tex]
In the given function, a=-5, b=15, c=20. So,
[tex]-\dfrac{b}{2a}=-\dfrac{15}{2(-5)}=\dfrac{15}{10}=1.5[/tex]
Put x=1.5 in the given function.
[tex]h=-5(1.5)^2+15(1.5)+20[/tex]
[tex]h=31.25[/tex]
Therefore, the maximum height of the flare is 31.25 metres and t=1.5 seconds.
