Final answer:
The equation of the parabola with vertex (2.5, 2.75) that passes through the point (1, 5) is y = (x - 2.5)^2 + 2.75.The parabola's equation, y = (x - 2.5)^2 + 2.75, captures its vertex at (2.5, 2.75) and ensures passage through (1, 5), fulfilling the given conditions precisely.
Step-by-step explanation:
To write the equation of a parabola that has a vertex of (2.5, 2.75) and passes through the point (1, 5), we can start by using the vertex form of a parabola's equation, which is:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola. Plugging our vertex in, we get:
y = a(x - 2.5)^2 + 2.75
Since the parabola passes through the point (1, 5), we can substitute x with 1 and y with 5 to solve for 'a':
5 = a(1 - 2.5)^2 + 2.75
5 = a(-1.5)^2 + 2.75
5 = a(2.25) + 2.75
2.25 = a(2.25)
a = 1
Now, we can write the final equation of the parabola:
y = (x - 2.5)^2 + 2.75
This gives us the required parabolic equation with a vertex at (2.5, 2.75) and passing through the point (1, 5).