f(x) = x^2 + 2x - 3. Where does the graph of the function f intersect the x-axis?

First, let's use the discriminant to check that the function actually does intersect the x-axis. b²-4ac = 4-(4 x -3) = 4+12 = 16, which is greater than 0, so we're fine.
The function intersects the x-axis whenever f(x) = 0, so we need to solve the equation "x² + 2x - 3 = 0" for x.
There are two methods we could use. First we could factorise the equation: x² + 2x - 3 = (x-1)(x+3) = 0, so x = 1 or -3
Or we could use the quadratic equation: x = (-b ± sqrt(b²-4ac)) / 2a = (-2 ± sqrt(16))/2 = (-2 ± 4) /2 = -1 ± 2 = 1 or -3
So either way, we get the same answer: x = 1 or -3.
You can try checking that this answer is correct by substituting "1" or "-3" for "x" in the equation x² + 2x - 3 and making sure that you get "0"