y = x²y = 2x + 1
Here's the picture: the parabola y = x² and the line y = 2x + 1 meet where their y-values are equal, so x² = 2x + 1. Rearranging gives x² − 2x − 1 = 0, and the quadratic formula gives x = 1 ± √2. That's about x ≈ 2.41 and x ≈ −0.41.
To get the points themselves, plug each x back into the line (it's the simpler equation). At x = 1 + √2, y = 3 + 2√2 ≈ 5.83. At x = 1 − √2, y = 3 − 2√2 ≈ 0.17. So the two meeting points are roughly (2.41, 5.83) and (−0.41, 0.17).
A good check for your son: substitute each point into both equations and confirm they match. Also, the line crosses the parabola twice because the discriminant is positive; a line that just touched the curve once would show a zero there.
