(1) Find the analytical expression of this parabola.
(2) Let the vertex of the parabola be D, point P be on the axis of symmetry of the parabola, and ∠PAD=∠ACB, and find the coordinates of point P.
(1) Let the abscissas of A and B be M and N respectively, then Mn >；; 0,
B=4 When the symmetry axis is a straight line x=4,
The symmetry axis is on the right side of the y axis,
∴m>； 0，n & gt0,
M+n=8 Judging from the meaning of the question,
mn=2c，
m=c
The solution is m=6, n=2, c=6,
The analytical formula is y= 1/2X? -4X+6
(2) It can be seen from the image that ∠ ABC = ∠ Abd = 45,
When p is higher than d, ∠ BDP = 45 = ∠ ABC,
If < ACB = < BPD,
Then △ABC∽△BDP
∴AB/DB=BC/PD，
∴BD=4，
If point p is lower than point d,
Then < DBP+< DPB = 45,
No internal angle equals ∠ABC, so a similar triangle does not exist.
To sum up, point P (4 4,4)