The grid lines in the graph below are one unit apart. The red parabola shown is the graph of the equation $y = ax^2 + bx + c.$ Find $a+b+c$.
https://latex.artofproblemsolving.com/c/e/2/ce264d13e5e7038f82ba3bae952d91fdf182b0ff.png
The y intercept is (0, 5)....so "c" = 5
The vertex is (2,1)
The coordinate of the vertex is
-b/[ 2a ] = 2
-b = 4a
b = - 4a
And (1,2) is on the graph....so we have that
2 = a(1)^2 - 4a(1) + 5
2 = a - 4a + 5
-3 = -3a
1 = a
So b = -4(1) = -4
a + b + c = 1 - 4 + 5 = 2
