Answer:
y = (1/3)(x +2)(x -3)
Explanation:
You want an equation for the quadratic whose graph has x-intercepts (-2, 0) and (3, 0), and y-intercept (0, -2).
X-intercepts
When a polynomial function has a zero at x=q, it means it has a factor of (x -q). Here, the zeros are given as x=-2 and x=3, so the function will have factors ...
(x -(-2)) = (x +2), and
(x -3)
Y-intercept
The y-intercept is the constant term in the product ...
y = a(x +2)(x -3) . . . . . . . product of factors of the quadratic
y = a(x² -x -6) = ax² -ax -6a
The constant term is -6a, and we want to choose the value of 'a' to make it be -2:
-6a = -2
a = -2/-6 = 1/3 . . . . . divide by the coefficient of 'a'
The equation can be written as ...
y = 1/3(x +2)(x -3)