# Porabola Example

- Question:
- 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:

- 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:

- 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 => x
_{1} = 3
- solution2: x - 1 = -2 => x = 1 - 2 = -1 => x
_{2} = -1
- so the length of AB = | x
_{1} - x_{2} | = | 3 - (-1) | = | 3 + 1 | = 4