+447 The parabola $y = ax^2 + bx + c$ is graphed below. Find $a \cdot b \cdot c.$ (The grid lines are one unit apart.)
The graph passes through (-3,5), (-1,7), and (2,-1).
+129771 a(-3)^2 - (3)b + c = 5
a(-1)^2 - 1b + c = 7
a(2)^2 + 2b + c = -1
9a - 3b + c = 5 (1)
1a -1b + c = 7 → -1a + 1b - c = -7 (2)
4a + 2b + c = -1 (3)
Add (1),(2)
8a -2b = -2 → 4a - b = -1 → b = 4a + 1 (3)
Add (2) , (3)
3a + 3b = -8 (4)
Sub (3) into 4
3a + 3(4a + 1) = -8
15a + 3 = - 8
15a = -11
a = -11/15
b = 4(-11/15)+ 1 = -29/15
a - b + c = 7
(-11/15) - (-29/15) + c =7
18/15 + c = 7
c = 105/15 - 18/15 = 87/15 = 29/5
a* b * c = (-11/15)(-29/15)(29/5) = 9251 / 1125
