Solve and explain, that's what we're here for.
We're asked for the intersection of a line and a parabola; there may be zero, one or two intersections. We can write the quadratic and examine its discriminant.
x = 2y + 5
It's probably easier if we do y as a function of x.
x - 5 = 2y
y = (x-5)/2
That's equal to
y = (2x - 3)(x + 9)
(x-5)/2 = 2x² + 15x - 27
x - 5 = 4x² + 30x - 54
0 = 4x² + 29x - 49
Discriminant is d=b²-4ac = 29² - 4(4)(-49). Since ac<0 we get d>0 so two solutions.
Answer: C) 2
We could solve the equation with the quadratic formula but they didn't ask so we won't.
