how many times does the graph of

y= 2x squared -2x+3 intersect the x-axis?

It intersects the x-axis when y = 0.
So:

y = 2x^2 - 2x + 3
0 = 2x^2 - 2x + 3
Its not factorable so you'll have to use the quadratic equation to solve for x.

To solve for x, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In the given equation, a = 2, b = -2, and c = 3. Substituting these values into the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4 * 2 * 3)) / (2 * 2)
x = (2 ± √(4 - 24)) / 4
x = (2 ± √(-20)) / 4

Here, we encounter a problem. The square root of a negative number (-20 in this case) is not a real number. This means that the quadratic equation has no real solutions, and therefore the graph of y = 2x^2 - 2x + 3 does not intersect the x-axis.