Question

How many solutions exist for the mixed-degree system graphed below?

A straight line a parabola are on a coordinate plane. The line is horizontal to the x-axis at y = 2. The parabola opens down and its vertex intersects with the straight line at (2, 2). The parabola also goes through (0, negative 3) and (4, negative 3).
zero
one
two
three

Answer 1

One.

Since the vertex is at (2,2) and the parabola opens downward, the horizontal line y = 2 touches the parabola only at its vertex. Algebraically, with parabola y = a(x−2)^2 + 2 and (0,−3) giving a = −5/4, solving 2 = −5/4(x−2)^2 + 2 yields (x−2)^2 = 0, so x = 2 (one intersection).