Given the parent function f(x)= x^2, write in 3 different forms
a) In Vertex Form f(x)= a(x-h)^2+k
b) In Standard Form f(x)= ax^2+bx+c
c) In Factored Form f(x)= a(x-r)(x-r)
The points on the graph were
(3,0)
(4,-1)
(5,0)
+23246 If you graph these three points and draw a parabole that passes through these points, you will see that
-- the vertex occurs at (4, -1)
-- that the value of a must be 1:
a) f(x) = 1(x - 4)2 - 1
Multiplying this out: (x - 4)2 - 1 = x2 - 8x + 16 - 1 = x2 - 8x + 15
b) f(x) = 1x2 - 8x + 15
Factoring: x2 - 8x + 15 = (x - 5)(x - 3)
c) f(x) = 1(x - 5)(x - 3)
