Answer:
y=-3.5(x−5)^2+17
Explanation:
Let's assume that since this equation has a vertex that it is a parabola with the form y = ax^2 + bx + c.
Let's rewrite it in vertex form as:
y=a(x−h)^2+k
where h and k are the horizontal (h) and vertical (k) coordinates of the vertex.
The vertex of (5,17) gives us both h (5) and k (17), Substituting these values gives us:
y=a(x−5)^2+17
To find a, use the one given point the parabola intersects (11,-109) and solve for a:
y=a(x−5)^2+17
-109=a((11)−5)^2+17
-109=a(6)^2+17
-109-17=a(36)
36a = -126
a = -3.5
This leads us to:
y=-3.5(x−5)^2+17
See the attached graph.