The analytic expressions of quadratic decomposition function and linear function are obtained by using undetermined coefficient method, focusing on the properties of similar triangles, Pythagorean theorem, the judgment and properties of rectangle, the properties of isosceles right triangle, and the analytical expressions of functions when solving.

The first question needs to pass through point C according to the known conditions, set the analytical formula of parabola as y=ax2+bx+2, and then get the result according to points A and B;

The second problem is that △ABE with a and b as right-angle vertices does not exist, so △ABE can only be a triangle with point E as right-angle vertex.

The third problem, as shown in Figure 2, is to connect AC, so that the DE⊥x axis is at point E, BF⊥ad is at point F, BC∑AD is assumed to be y=kx+b, and AD is assumed to be Y = Kx+N. By using the undetermined coefficient method, the analytical expression of a linear function can be obtained, so that the coordinates of point D can be obtained.

Solution: (1)∫ The parabola passes through point C (0,2),

∴ Let the analytical expression of this parabola be y = AX2+BX+2.

Substitute A (- 1, 0) and B (4, 0).

This is a detailed answer/exercise/math /798568, which contains detailed ideas and answering process. Known parabola y=ax? +bx+c(a≠0) passes through a (- 1, 0), b (4 4,0) and c (0,2).

(1) Find the analytical expression of this parabola;

(2)E is a moving point on a parabola. Is there a point e that makes a triangle with vertices a, b and e similar to △COB? If it exists, try to find the coordinates of point e; If it does not exist, please explain the reason;

Honey, if you don't understand, you can keep asking me. Come on ~ I hope it can be adopted if it helps!