parabola

Y = x 2-bx+c, and the x axis is at point a (1, 0).

∴ 1-b+c=0，

axis of symmetry

x=b/2=2，

The answer is b=4, c=3,

figurative

Analytical formula

Y = x 2-4x+3。

(2) the symmetry point b' of b (0,3) about the symmetry axis x=2 is (4,3),

∴pa+pb=pa+pb'>； =AB', when a, p, b'

Three-point line

Take the equal sign,

At this time, the perimeter of △PAB is the smallest, and the coordinate of P is (2, 1).