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. NOTE: the answer isn’t -3.
1. The parabola is y = 1/4*x^2 - 3x + 9, so a + b + c = 1/4 + (-3) + 9 = 25/4.
2. The equation of the parabola is y = 2x^2 - 4x + 7, so a + b + c = 5.
+128399 The vertex is ( 2,1) = (h, k)
Note that if we have the form
y = a(x -h)^2 + k substituting the vertex coordinates into this we have
y = a(x - 2)^2 + 1
Since the point (0, 5) is on the graph we have that
5 = a( 0 - 2)^2 + 1
5 = a(-2)^2 + 1
4 = 4a
a = 1
So we have this
y = 1 ( x - 2)^2 + 1
y = 1x^2 - 4x + 4 + 1
y = 1x^2 - 4x + 5
a = 1
b = -4
c =5
a + b + c =
1 - 4 + 5 =
2
