Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), vertical axis of symmetry, and contains the point (2,0).
+128407 Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), vertical axis of symmetry, and contains the point (2,0).
(2.0) means that x = 2 is a root
The x value of the other root is given by
[ 2 + x ]
_______ = 5 multiply through by 2
2
2 + x = 10 subtract 2 from both sides
x = 8
So.....the other root is (8, 0)
So we have that
y = a (x - 2) (x - 8) and since (5,3) is on the graph, we can find "a" as
3 = a ( 5 - 2) (5 - 8)
3 = a (3)(-3)
3 = - 9a
a = -1/3
So we have that
y = (-1/3) (x - 2) (x - 8)
y = (-1/3) (x^2 - 10x + 16)
y = (-1/3)x^2 + (10/3)x - (16/3)
So a + b + c = (-1/3) + (10/3) - (16/3) = -7/3
