Porabola Example

Question:
Parabola example
The function y = f(x) given above, find
(1) the axis of symmetry and vertex.
(2) if the function y = f(x) intercepts the x-axis at point A and B, find the length of AB.
Solution:
Using quadratic equation to solve parabola problem.
Analysis (1)
For the parabola function: y = a(x - h)2 + k, its vertex is (h, k) and the symmetry axis is x = h.
In this case, y = (1/2)(x - 1)2 - 2, its vertex is (1, -2) and symmetry is x = 1.
Its graph is:
graph of the parabola function.
Analysis (2)
To find the x-intercept, let y = 0
(1/2)(x - 1)2 - 2 = 0
(1/2)(x - 1)2 = 2
(x - 1)2 = 4
solution1: x - 1 = +2 => x = 1 + 2 = 3 => x1 = 3
solution2: x - 1 = -2 => x = 1 - 2 = -1 => x2 = -1
so the length of AB = | x1 - x2 | = | 3 - (-1) | = | 3 + 1 | = 4