Hint (3)① Find ∠MCH =∠ Cao Can according to the equal correspondence angle of similar triangles, and then (i) When point H is below point C, the CM∨x axis can be determined by using the equal correspondence angle, so that the ordinate of point M is the same as that of point C, which is ∠ 2, and it can be calculated by substituting it into the parabolic analytical formula; (2) When the H point is above the C point, according to the conclusion of (2), the M point is another intersection of the straight line PC and the parabola, and the analytical expression of the straight line PC can be solved simultaneously with the analytical expression of the parabola, thus obtaining the coordinates of the M point.

Analysis (3)①∫△CHM∽△AOC, ∴∠MCH=∠CAO

(i) As shown in Figure 1, when H is lower than point C,

∠∠MCH =∠CAO，

∴CM∥x axis,

The ordinate of point m is -2,

∴x？ ﹣x﹣2=﹣2，

The solution is x 1=0 (excluding), x2= 1,

∴M( 1,﹣2)，

(2) As shown in Figure 1, when H is above point C,

∠∠MCH =∠CAO，

Pa = PC, which is obtained from (2), and m is the other intersection of the straight line CP and the parabola.

Let the analytical formula of the straight line CM be y = kx-2,

Substituting the coordinates of p (3/2,0) gives 3/2 k-2 = 0.

The solution is k=4/3,

∴y=4/3x﹣2，

From 4/3 x to 2 = x? ﹣x﹣2，

The solution is x 1=0 (excluding), x2=7/3,

At this time y= 10/9,

∴m′(7/3, 10/9)