would someone mind explaining how to find the maximum or minimum of

y=x^2-2x-48

All quadratics graph as parabolas. The parabola either opens up or down, depending on the sign of leading coefficient (the coefficient of the x^2 term).

The max or min value of the function is at the vertex of the parabola. The vertex is a minimum for parabolas that open upward (is U-shaped, having a positive leading coefficient).

The vertex gives the maximum value if the parabola opens downward. Make sense?

The x value of the vertex is “-b/2a”, where “a” is the leading coefficient and “b” is the coefficient of the x term. In your problem, a = 1 and b = -2.

After finding the x value of the vertex, plug that x value into the equation to find the y value. This value is either your maximum or your minimum.