It is known that the parabola y 1 4x 2 and the straight line y ax 1 1 are verified

2) Combine the linear equation with the parabolic equation and subtract y:

x²-4ax-4=0

According to Veda's theorem: x1+x2=4a, x1x2=-4, according to the midpoint coordinate formula, the coordinates of point p are ((x1+x2) 2,(y1+y2) 2)y1+y2=ax1+1+ax2+1=a(x1+x2)+2=4a +2p(2a,2a +1).

3) x1-x2 =(x1+x2) -4x1x2=16a +16, so d=4(a+1).

4) The distance from P(2A,2A +1) to the straight line y=-1 is 2a +2 =2(A +1), and the radius of the circle r=d 2=2(A +1), so the distance from the center of the circle to the center of the circle is equal to the radius, so the straight line is tangent to the circle.

solution, simultaneous y=1 4x 2 and y=ax+1

Finishing wait until 1 4x 2-ax+1=0

By the relation between the root and the coefficient, x1 + x2 = 4a

The x-coordinate of the focus (x1+x2) 2=2a

Coordinates of y y=2a 2+1

Midpoint (2a, 2a 2+1).

3,x1x2=4 x1+x2=4a

x1-x2) 2=(x1+x2) 2-4x1x2=16a 2-16d=4x(1+a2) under the root number multiplied by (a2-6) tangent.

Substituting the point into the split gives -3=9a, i.e. a=-1 3. Analytic formula: y=-1 3(x+2) 2The axis of symmetry is x=-2, and the vertex Sun Fu sits on the Kai Sui mark (-2,0).

1) According to x=1, y=-3, substituting the equation is.

a(1+2), know. a

2) (3) This is a parabolic abolisher with an opening downward, an axis of symmetry of x=-2, and a vertex of (-2,0).

4) Because the opening is downward, on the left side of the Tongcha axis of symmetry, y increases with the increase of x, that is, when x<=2, y increases with the increase of x. Hail wheel knows.

Substituting x=1 and y=3 into the parabola yields: a=1

The number of the chamber is parsed and the circle is y=x branch or.

When y=27, x=3 times the root number 3

i.e. 2=a*(-1).

a=2, so y=2x

So y=4 then 2x =4

x = 2, so x = 2

x=-(-4)/2=2

x=2 is substituted for y=-4x-1

y=-9x=2, y=-9 is substituted into y=x 2-4x+m

This gives -9=4-8+m

m=-5 The analytic formula of this parabola y=x -4x-5

From the inscription, the vertex coordinates of the parabola y=x 2-4x+m can be found as (2,m-4), and the coordinates of this point are brought into the line y=-4x-1.

m-4=-4*2-1

m=-5, so the analytic formula for the parabola is y=x, 2-4x-5

The calculations aren't necessarily correct, but that's the way of thinking.

x=-b/2a =2

So the x=2 of the vertex is then substituted y=-4x-1 to get y=-9, so the vertex (2,-9).

Then substitute the parabola to find m

Hit slowly--

y=1 4x +x+m, right?

Formula, y=1 4(x+2) +m-1

The vertices are (-2, m-1).

Substituting the straight line yields: m-1=-2+3

Obtain: m=2 so the parabola is y=1 4x +x+2

1、-4=a(-2)²

a=-1y=-x²

When x=-3, y=-9

-3, -8) is not on the image.

The coordinates of point b are (2,-4).

The distance from ab=4o to ab is 4

s=4×4/2=8

Top: When x>0, y increases with the increase of x, when x <0, y decreases with the increase of x: when x>0, y decreases with the increase of x, and when x<0, y increases with the increase of x.

4 = 3x x = 3 4 (miscalculated here).

x= 2/3 of the root number