Wang Qiang hit the ball somewhere during a golf practice, and the route of the ball flight was satis

In a golf practice, Wang Qiang hit the ball somewhere, and its flight path satisfies the parabola, where y(m) is the flight height of the ball, and x(m) is the horizontal distance of the ball, and the result is that the ball is still 2m away from the horizontal distance of the hole.

1) Please write the vertex coordinates of the parabola;

2) the maximum horizontal distance of the flight of the requested ball;

3) If Wang Qiang hits the ball from here again, if he wants the maximum height of the ball to fly unchanged and the ball just enters the hole, what kind of parabola should the ball's flight path meet, and find its analytical formula.

Solution: (1) y=x2+ x =(x-4)2+ and the vertex coordinates are (4,).

2) Let y=0, x2+ x=0, and solve x1=0, x2=8, so the maximum horizontal distance of the ball flight is 8 meters

3) Just into the hole, then the parabola needs to pass through the (0,0) on the x-axis,(10,0) the height of the ball flight is unchanged, then the ordinate of the highest point is, the vertex coordinate of the parabola is (5,, let the analytical formula of the parabola be y=a(x-5)2+, through (0,0),25a+, a=,y=

Speechless! Ask you don't know anything!

Solution: (1) In RT AOC, AOC=30° ,OA=8 root number 3, AC=OA·sin30°=8 root number 3 root number 3, OC=OA·COS30°=8 root number 3 2 root number 3=12 The coordinates of point A are (12,4 root number 3) Let the analytical formula of OA be y=kx, and substitute the coordinates of point A (12, 4 root number 3) to obtain: 4 followed by 3=12k , k = 3 of the root number of 3 points, and the analytical formula of OA is y=3 of the root number 3 times x; (2) The coordinates of vertex b are (9,12) and the coordinates of point o are (0,0) Let the analytic formula of the parabola be y=a(x-9) 2+12, and substitute the coordinates of the point o into :

0=a(0-9) 2+12, the solution is a=minus 4/27, and the analytic formula for the parabola is y=minus 4/27(x-9) 2+12 and y=minus 27/4x 2+8/3; (3) When x = 12, y = 32/32≠ 4 number 3, Xiao Ming cannot play the golf ball directly from point O to point A of hole A

.Solution: (1) In RT AOC, AOC=30 O, OA=8, AC=OA·Sin30O=8 =, OC=OA·COS30O=8 =12

The coordinates of point A are (12,).

Let the analytic formula of oa be y=kx, and substitute the coordinates of the point a(12,) into the :

12k, k= ,oa is y=x;

2) The coordinates of vertex b are (9,12) and the coordinates of point o are (0,0) Let the analytic formula of the parabola be y=a(x-9)+12, and substitute the coordinates of the point o into :

0=a(0-9)+12, the solution is a= , and the analytic formula of the parabola is y= (x-9)+12

and y= x+ x;

3) When x=12, y= , Xiao Ming can't hit the golf ball directly from point O to point A of hole A

Solution: (1) The opening is downward, and the vertex coordinates are <>

The axis of symmetry is x=4;

2) Let y=0 get <>

Solution: x10, x2

8. The maximum horizontal distance of the ball flight is 8m;

3) For the ball to be just hole-in-the-hole and the maximum height of flight remains the same, the maximum horizontal distance of the ball is 10m, the axis of symmetry of the parabola is x=5, and the vertex is <>

In this case, the analytic formula of the corresponding parabola is <>

Point (0,0) on this parabola, <>

a=<>

i.e. <>

1) Shouted by the title and pinned Zheng You.

x=-b2a

Substitute x=4. y=-1

x2x solution yields y=4

The coordinates of the parabolic vertex are (4,4) (1 minute).

x2x=02 points).

x10，x2

8. The maximum horizontal distance of the ball flight is 8m (2 points).

3) According to (1) the maximum height of the ball is 4 when x = 4, when the ball is just in the hole, i.e. (10, 0), the apex of the shed branch is (5, 4) (3 points).

100a+10b=0，25a+5b=4a=-4b=8

4 points) The path of the ball satisfies the analytic formula of the parabola as y=-4x

x (5 points).

1) From the meaning of the title.

x＝?b2a

Substitute x=4. y＝?1

x2x solution yields y=4 parabolic vertex coordinates as (4, Zen Tong 4) (1 point) x2x 0

2 points) x10, x28, the maximum horizontal distance of the ball flight is 8m He Qingtan cha (2 points) 3) According to (1) when x = 4, the maximum height of the ball is 4, at this time the ball is just hole-in, i.e. (10, 0), and the apex is (5, 4) (3 points).

100a+10b=0，25a+5b=4a＝?4b＝8

4 points) The path of the ball's flight satisfies the analytic formula of the parabola as y ?4x

x (5 points).

Solution: (1) In RT AOC, AOC=30°, OA=8AC=OA sin30°=8

oc=oa•cos30°=8

The coordinates of point A are (12,4

3. Let the analytic formula of oa be y=kx, and substitute the coordinates of the point a(12,4 to get :

12k，k=

The analytic formula for OA is y=

x；2) The coordinates of vertex b are (9,12), and the analytic formula of the parabola is y=a(x-9).

12, the coordinates of the point o are (0,0).

Substituting the coordinates of the point o yields:

0=a（0-9）

12, the solution is a=-

The analytic formula for the parabola is y=-

x-9) i.e. y=-

xx；3) When x=12, y=

Xiao Ming's shot can't hit the golf ball directly from point O to point A of the hole

Solution: (1) In RT AOC, AOC=30 O, OA=8, AC=OA·Sin30O=8 =, OC=OA·COS30O=8 =12

The coordinates of point A are (12,).

Let the analytic formula of oa be y=kx, and substitute the coordinates of the point a(12,) into the :

12k k=

The analytic formula of OA is y=x;

The coordinates of vertex b are (9,12) and the coordinates of point o are (0,0) Let the analytic formula of the parabola be y=a(x-9)+12, and substitute the coordinates of point o into :

0=a(0-9)+12, the solution is a=

The analytic formula for the parabola is y=-

x-9)+12 and y=x+

x；When x=12, y=

Xiao Ming's shot can't hit the golf ball directly from point O to point A of the hole

ocoacos30 degrees = 12,ac

oasin30“a（12,4√3）

OA of the slope of the straight line

3 3 and the straight line oa by the origin, the analytic expression of oa, the vertex coordinates of the y parabola (9, 12).

Therefore, it has an analytical formula y

a（x-9）^

0,0) into 0

Solution, for a

4 27 Analytic formula y for parabola

4/27（x-9）^

br> a(12,4 3) substitute the parabola of the formula to see if it conforms. Bring x

y is not equal to 32 3

(1) In RT AOC, AOC=30°, OA=83, AC=OA?sin30°=83×1

2=43，oc=oa?cos30°=83×

The coordinates of the point A are (12,43), and the solution of Oa is y=kx, and the coordinates of the point A (12,43) are substituted into the coordinates: 43

12k，∴k=

Answer: <>

Solution: (1) According to the problem: ACP=90°, APC=30°, PA=8 gear collapse cos apc=oc

oapc=8

cos30°＝12

The length of the PC is 12m

2) With p as the origin and the straight line where PC is located as the x-axis, the planar Cartesian coordinate system as shown in the figure is established, and it can be seen that the vertex b(9,12), the parabola passes through the origin, and the analytical formula of the parabola is y=a(x-9)2

12. Substituting the coordinates of the point p(o,0) into the feasible circle obtains: 0=a(0-9)212, and obtaining a ?4

Therefore, the analytic formula of the parabola is: y=-4

x?9) 3) From (1) the coordinates of point c are (12,0), and AC 4 is easy to find, and the coordinates of point A are (12,4

3) When x=12, y=4

Neutral. Therefore, Xiao Ming cannot hit the golf ball directly from point P into hole A with one stroke