a quadratic function is written in the form f(x)=a(x-m)(x-n) . the graph of f passes through the points (0,-16),(4,0), and (12,0). what is the value of a
-16 = a(-m)(-n) = a m n
0 = a(4-m)(4-n) =so 0 = 16 - 4 m - 4 n + mn
0 = a(12-m)(12-n) = 144 -12 m - 12 n + mn
so
48 - 12 m - 12 n + 3 mn = 144 - 12 m - 12 n + mn
2 mn = 144 - 48 = 96
mn = 48
so
-16 = a mn = 48 a
a = -16/48 = -1/3
(4,0), and (12,0) are the x-intercepts, so x=4 and x=12
equation:
f(x) = a(x-4)(x-12)
but (0,-16) also lies on it, so
-16 = a(-4)(-12)
a = -16/48 = -1/3
f(x) = (-1/3)(x - 4)(x - 12)