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Interpreting the problem of overtraining in ninth grade mathematics
Parabola y= 1/2x2+bxx axis intersects at A.B and the positive half axis of y axis intersects at c, OB=OC, and its symmetry axis is straight line x=4.

(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)