Consider the quadratic equation y=x 2 −2x+3. Find the x−intercepts of the graph of the quadratic relationship.

The x-intercepts of a graph are the points where the graph crosses the x-axis. For a quadratic equation, these are the values of x for which y = 0.

So, to find the x-intercepts of the graph of the quadratic equation y = x^2 - 2x + 3, we set y = 0 and solve for x:

0 = x^2 - 2x + 3

This is a quadratic equation, which can be solved using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / (2a)

In this case, a = 1, b = -2, and c = 3. Substituting these values into the quadratic formula gives:

x = [2 ± sqrt((-2)^2 - 413)] / (2*1) x = [2 ± sqrt(4 - 12)] / 2 x = [2 ± sqrt(-8)] / 2

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the graph of the quadratic equation y = x^2 - 2x + 3 does not cross the x-axis, and there are no x-intercepts.