Brainly doesn't automatically "know" every part of the problems you post here; you have to ensure that your post includes everything in the original problem.
We can still have some fun with answer choice x = 1, x = 3:
An associated quadratic function would have the form y = a(x-1)(x-3). Just supposing that the point (2, 5) were on the graph, then this y = a(x-1)(x-3) would become 5 = a(2-1)(2-3), or 5 = a(1)(-1), or 5 = -a, or a = -5.
Thus, the equation of the parabola would be y = -5(x-1)(x-3), or, in the more usual form, y = -5(x^2 - 4x + 3).
Complete the square to find the vertex:
Steal y = x^2 - 4x + 3 for a moment and complete the square:
x^2 - 4x + 3 = x^2 - 4x + 4 - 4 + 3, or (x-2)^2 - 1
Subbing this back into y = -5(x^2 - 4x + 3), we get
y = -5 [ (x-2)^2 -1 ], or y = -5(x-2)^2 + 5. This shows that the vertex is at (2, 5), that the graph opens downward, and the graph is symm. about the line x = 2.
Having fun yet?
