Find the coordinates of the vertex of the parabola y=x²-8x+2

There are a few ways to do it. Here's how I would get it. Take the derivative and set it to zero and solve for x. That gives the x coordinate of the vertex. Then plug that x value in the function to see which y value corresponds. The derivative is given by

y'=2x-8

So set it to zero and get x

2x-8=0

2x=8

x=4

Now put x=4 in your original function

4^2-8 (4) + 2=-14

So the vertex is at (4, - 14)