Answer: [tex]y = -\frac{8}{9} (x-15)^2+200[/tex]
Step-by-step explanation:
To answer this, we have to use quadratic equations.
We can represent this by using information given to us.
Knowing that a parabola peaks at its vertex, and the flare goes from its launch site (x = 0) and hits the ground 30m from the launch site (x = 30), we know that the flare peaks 15 meters away horizontally from the launch point.
We also know that the y-intercept is 0, because it is fired from the ground.
Knowing that the vertex for the parabola is (15, 200) and the y-intercept is (0, 0), we can model an equation.
Vertex form is:
[tex]y = a(x-h)^{2} + k[/tex], where (h, k) is the vertex.
[tex]y = a(x-15)^2+200[/tex]
We can plug the y-intercept, (0, 0), into this equation to find a:
[tex]0 = a(-15)^2 + 200\\0 = 225a+200\\a = -\frac{8}{9}[/tex]
