Answer
Vertex: (1,0)
Axis of symmetry: x=1
Graph opens upward.
Work Step by Step
Equation: f(x)= (x-1)^2
To find the vertex, you must first find your A, B, and C values of the equation. In order to do this, you must use the foil method (x-1)(x-1) which comes out to be
x^2-2x+1.
The A= 1, B= -2, and C= 1.
To find the x value of the vertex, x= -B/2A. so..
x= -(-2)/2(1)
x= 2/2
x=1
Now plug the x value we just found into the equation.
f(0)= 0^2-2(0)+1
f(0)= 0-0+1
f(0)= 0+1
f(0)= 1
So the vertex is (1, 0)
To find the axis of symmetry, the formula x= -B/2A can be used again. so..
x= -(-2)/2(1)
x= 2/2
x=1
so the axis of symmetry is x=1.
The graph opens upward because the A value is greater than 0.
To graph the equation we must find two more points. Any number can be plugged into the equation, but I'm using 1, -1.
(1)^2-2(1)+1= f(1)
1-2+1= f(x)
-1+1= f(x)
0= f(x)
so (1,0) is a point on the graph.
(-1)^2-2(-1)+1= f(-1)
1+2+1= f(-1)
4= f(-1)
So (-1,4) is the other point on the graph.
