Final answer:
The question appears to contain an error regarding x-intercepts. Assuming they are points on the parabola, the parabolic equation can be found with further clarification using the vertex form y = a(x-1)^2 + k and the given point (4,8).
Step-by-step explanation:
The question asks for the equation of a parabola with specific x-intercepts and that passes through a given point. Given x-intercepts at (1, √5) and (1, -√5), there seems to be a misunderstanding as these cannot be x-intercepts since they don't have y=0. However, assuming these are points on the parabola, since the x-coordinates are the same, the axis of symmetry is x=1. The standard form of a parabolic equation is y = ax2 + bx + c. Since the axis of symmetry is x=1, this can be rewritten as y = a(x-1)2 + k, where (1, k) is the vertex of the parabola.
To find 'a', we can use the point (4,8) which lies on the parabola. Plugging this into the vertex form we get:
8 = a(4-1)2 + k
Since 32 = 9, this can be simplified to:
8 = 9a + k
We need another equation to solve for 'k' but to do that we have to clarify the given points or the context of the problem.
Once 'a' and 'k' are known, the parabolic equation can be fully determined. This explanation uses concepts such as quadratic equations, axis of symmetry, and vertex form which are important in solving for the parabola's equation.