Answer:
y = -2x² + 12x - 16
Explanation:
The graph appears to be an inverted parabola.
The equation of a parabola is
y = ax² + bx + c
Use point (3, 2).
2 = a(3²) + b(3) + c
9a + 3b + c = 2 Eq. 1
Use point (2, 0).
0 = a(2²) + b(2) + c
4a + 2b + c = 0 Eq. 2
Use point (4, 0).
0 = a(4²) + b(4) + c
16a + 4b + c = 0 Eq. 3
We have a system of three equations in three unknowns, a, b, and c.
9a + 3b + c = 2
4a + 2b + c = 0
16a + 4b + c = 0
Subtract Eq. 2 from Eq. 1.
Subtract Eq. 2 from Eq. 3
5a + b = 2
12a + 2b = 0
-10a - 2b = -4
(+) 12a + 2b = 0
-----------------------------
2a = -4
a = -2
5(-2) + b = 2
b = 12
9a + 3b + c = 2
-18 + 36 + c = 2
c = -16
y = -2x² + 12x - 16