It s a hard math problem to write the process of being squared by K and squared by X

Solution:1Because the point a(-1,-1) is on the parabola.

So k 2-1 + 2k - 4 + 1 = -1

k^2+2k-3=0

k+3)(k-1)=0

k1=-3,k2=1

And because k 2-1≠0

i.e. k≠ 1, so k=-3

So the analytic formula of this function is: y=8x 2+10x+1, the axis of symmetry is: straight line x=-10 16=-5 8

2.exists, and the analytic formula for this line is: 5 8x+y+69 32=0 let y=-1, i.e., 8x 2+10x+1=-1

x+1)(4x+1)=0

x1=-1,x2=-1/4

Because point b is symmetrical with point a with respect to the axis of symmetry.

So b(-1 4,-1).

Because the straight line only intersects the parabola one point.

So this line is the tangent of the parabola at point b.

Because y = 16x+10

Let y = 0, x = -5 8

So y-(-1)=-5 8[x-(-1 4)] i.e. 5 8x+y+69 32=0

Solution: k2-1+2k-4+1=-1, get k=-3 or 1 (rounded, because the curve is parabolic), so the parabolic equation is y=8x2+10x+1

The axis of symmetry is x=2(k-2) 2(k2-1)=(k-2) (k2-1)=-5 8

b is (-11 8, -1).

This line exists: when the line is parallel to the y-axis, the line is x=-11 8;

If the straight line is a tangent through point b, the slope of the derivative is k=16*(-11 8)+10=-12

So the straight line is y+1=-12(x+11 8).

If you miscalculated, do it again.

k2-1+2k-4+1=-1, we get k=-3 or 1 (rounded off because the curve is parabolic), so the parabolic equation is y=8x2+10x+1

The axis of symmetry is x=2(k-2) 2(k2-1)=(k-2) (k2-1)=-5 8

b is (-1, 4, -1).

This line exists: when the line is parallel to the y-axis, the straight line is x=-1 4, and if the straight line is a tangent line through point b, then the slope of the derivative is k=16*(-1 4)+10=-6

So the straight line is y+1=-6(x+1 4).

Solution:1Because the point a(-1,-1) is on the parabola, so k 2-1+2k-4+1=-1 k 2+2k-3=0 (k+3)(k-1)=0 k1=-3,k2=1 and because k 2-1≠0 i.e. k≠ 1 so k=-3 so the analytic formula of this function is:

y=8x 2+10x+1 The axis of symmetry is: straight line x=-10 16=-5 8 2Yes, this line is parsed by:

5 8x+y+69 32=0 Let y=-1, i.e. 8x 2+10x+1=-1 (x+1)(4x+1)=0 x1=-1,x2=-1 4 Because point b is symmetrical with point A with respect to the axis of symmetry, so b(-1 4,-1) Because the straight line only intersects the parabola at one point, this line is the tangent of the parabola at point b, because y =16x+10 makes y =0,x=-5 8 So y-(-1)=-5 8[x-(-1 4)] i.e. 5 8x+y+69 32=0