a+b+3=0
9a+3b+3=0
Solution, a= 1, b=-4.
So the analytic formula of quadratic function is y = x? -4x+3
(2) Because y = (x-2)? - 1
So the coordinate of point D is (2,-1).
In Rt△BOC, ob = 3, oc = 3, BC = 3 √ 2.
So △BOC is an isosceles right triangle.
△ABD, where AD = √ 2, BD = √ 2 and AB = 2.
Because, AD? +BD？ =AB？ , and ad = BD.
So △ABD is also an isosceles right triangle.
So, △ABD∽△BCO
(3) According to (2), ∠ OBC = ∠ Abd = 45.
Therefore ∠ CBD = ∠ OBC+∠ Abd = 90.
Extend CA and BD to point e.
By point a coordinates (1, 0) and point c coordinates (0, 3)
It can be concluded that the equation of the straight line where AC is located is y =-3x+3.
By point b coordinates (3,0) and point d coordinates (2, 1)
It can be concluded that the linear equation of BD is y = x-3.
Simultaneous two linear equations, the coordinates of point E are (3/2, -3/2).
In Rt△CBE, BC = 3 √ 2, BE = 3 √ 2/2.
Therefore, tan ∠ ACB = tan ∠ ECB = be/BC =1/2.
Let the coordinate of point P be (x, y), so that the perpendicular of the X axis passes through P and intersects the X axis at point F.
Then, that coordinate of point f is (x, 0).
In Rt△PFA, pf = | y | and af = x- 1.
So tan ∠ PAB = tan ∠ PAF = PF/AF = | Y |/(x-1).
Because ∠ Pabu =∠ACB.
That is, tan∠PAB=tan∠ACB.
Therefore |y|/(x- 1)= 1/2, that is, 2 | y | = x- 1.
Also, point P is the point on this quadratic function image, y = x? -4x+3
So, 2|x? -4x+3|=x- 1
Simplify it, 2x? -9x+7 = 0 or 2x? -7x+5=0
That is, (2x-7) (x- 1) = 0 or (2x-5) (x- 1) = 0.
Because point P and point A do not coincide, x≠ 1.
So, the solution is x = 7/2 or x = 5/2.
Accordingly, y = 5/4 or y =-3/4.
Therefore, the coordinates of point P are (7/2, 5/4) or (5/2, -3/4).