Given the x-intercepts "b" and "c", a quadratic equation can be expressed as
y = a(x -b)(x -c)
Since the values for the x-intercepts are known, the equation can be specified as
y = a(x +2)(x -3), which rules out the first two response options.
By substituting the point (x, y) = (-1, 2), we find
2 = a(-1 + 2)(-1 - 3) = -4a.
From this, when divided by -4, we conclude
a = -2/4 = -1/2, indicating the third option matches.
Thus, the correct answer is
y = -1/2 (x + 2)(x - 3)