Lianshan courseware mathematics

As shown in figure (1), in the plane rectangular coordinate system, the coordinate of point B of rectangular OABC is (4,3), the parabola passes through the vertices B, C, F (6 6,3) of rectangular ABCO, and the straight line AF intersects the Y axis at point E and BC at point D. 。

( 1)

Find the analytical expression of parabola;

(2) As shown in Figure (2), the moving point P starts from the point C and moves along the line segment CB to the end point B at a speed of/kloc-0 per unit length per second; At the same time, the moving point M starts from the point A and moves along the line AE at a speed of one second.

The speed of a unit length moves to the end e, the intersection p is PH⊥OA, the vertical foot is H, and MP is connected with MH. The movement time of point p is t seconds.

①

Let the area of △PMH be s, and find the functional relationship between s and t;

② Ask if EP+pH+HF has a minimum value, and if so, find the value of t; If not, please explain why.

Solution:

( 1)y=-x？ /2+2x- 1/2。

(2)

(1) At the same time, moving point M starts from point A and travels along line AE at a speed of one second.

The speed per unit length moves towards the end point e.

② The minimum value of EP+pH+HF is:

ED+DH'+H'F

=√[2? +(6-3)? ]+3+√[(6-2)? +3? ]

=√ 13+3+5