The graph of y = ax^2 + bx + c passes through points (0,5), (1,8), and (2,19). Find a + b + c.
+128448 y = ax^2 + bx + c
If the points passes through (0,5) then c = 5
So we have these two equations
a ( 1)^2 + b(1) + 5 = 8 → a + b = 3 → b = 3 -a (1)
a(2)^2 + b(2) + 5 = 19 → 4a +2b = 14 (2)
Sub (1) into (2) for b
4a + 2 ( 3 - a) = 14
4a + 6 - 2a = 14
2a = 8
a = 4 and b = 3 - 4 = -1
So the function is y= 4x^2 - x + 5
a + b + c = 4 - 1 + 5 = 8
