A math problem: improving the ability of top students to cultivate excellent teaching materials. Lecture 7, Group B, Question 8

Solution: Solution: (1) Establish a rectangular coordinate system with the positive semi-axis of point O as the origin and the ray OC as the y axis.

Let the resolution function of parabola be y=ax2,

The coordinates of point A are (4,8).

Point a is on a parabola,

∴8=a×42，

Solve a=,

The resolution function of parabola is: y = x2.

(2) find a way to:

Extend AC, pass through the parabola of the building shape at point D,

Then point a and point d are symmetrical about OC.

Connect BD and OC at point P, then point P is what you want.

(3) According to the meaning of the question, the abscissa of point B is 2.

Point b is on a parabola,

∴ The coordinates of point B are (2,2),

Similarly, the coordinate of point A is (4,8),

The coordinate of point ∴d is (∴ 4,8),

Let the resolution function of straight line BD be y=kx+b,

∴ ,

Solution: k =- 1, b = 4.

The resolution function of the straight line BD is y = x+4,

Substitute x=0 into y =-x+4, and the coordinate of point P is (0,4).

The materials used for the two columns are the most time-saving, and the distance between point O and point P is 4m. Agree 67| Comment (33)