The quadratic function y = 7x & sup2; - (K-2) x + k-1 is known. When the value of K is, the function takes the y-axis as the axis of symmetry. Write out the analytic expression of the function.)

The quadratic function y = 7x & sup2; - (K-2) x + k-1 is known. When the value of K is, the function takes the y-axis as the axis of symmetry. Write out the analytic expression of the function.)

When the parabola image is symmetric about the y-axis, it needs to satisfy that the coefficient of quadratic term is 0 (that is, it does not contain quadratic term)
therefore
-(k-2)=0
We get k = 2
So the analytic expression of the function is y = 7x & sup2; + 1

The analytic formula of quadratic function y = 4x ^ 2 + 8x is known. Write out the axis of symmetry and fixed-point coordinates of the function, and find the coordinates of the intersection of the image and the x-axis

y=4x²+8x+4-4
=4(x+1)²-4
So the axis of symmetry x = - 1
Vertex (- 1, - 4)
Y = 0 on X-axis
Then 4x & sup2; + 8x = 0
4x(x+2)=0
x=0,x=-2
So the coordinates of the intersection point with the X axis are (0,0), (- 2,0)