-b/2a= 1/2 ①

4a+2b-c=4 ②

∫x 12+x22 = 13 is equivalent to (x1+x2) 2-2x1x2 =13.

According to Vieta's theorem.

(-b/a)2-2c/a= 13 ③

Simultaneous solution of three equations

a= - 1 b= 1 c= - 6

∴y= - x2+x+6

(2) calculate B C according to the equation.

They are (3,0) (-2,0).

S△ABC= 10

Then S△PBC=5.

BC = 5

When p is on a straight line with y =±2, all meet this requirement.