Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,4), vertical axis of symmetry, and contains the point (1,0). What is (a,b,c)?
+128475 If it contains the point (1,0) then
a + b + c = 0
If the point (3,4) is the vertex than
-b/(2a) = 3
-b= 6a
b = -6a
Then
a(3)^2 + -6a(3) + c = 4
9a - 18a + c = 4
-9a + c = 4
c = 4 + 9a
So
a + b + c = 0
a + ( - 6a) + (4 + 9a) = 0
4a = -4
a = -1
b = -6(-1) = 6
c = 4 + 9(-1) = -5
{a , b , c} = { -1, 6 , - 5 }
