How do I convert the equation #f(x)=x^2-4x+3# to vertex form?

1 Answer
Jul 29, 2015

Answer:

#color(red)( f(x) = (x-2)^2-1)#

Explanation:

The vertex form of a quadratic is given by #y = a(x – h)^2 + k#, where (#h, k#) is the vertex.

The "#a#" in the vertex form is the same "#a#" as in #y = ax^2 + bx + c#.

Your equation is

#f(x) = x^2-4x+3#

We convert to the "vertex form" by completing the square.

Step 1. Move the constant to the other side.

#f(x)-3 = x^2-4x#

Step 2. Square the coefficient of #x# and divide by 4.

#(-4)^2/4 = 16/4 = 4#

Step 3. Add this value to each side

#f(x)-3+4= x^2-4x+4#

Step 4. Combine terms.

#f(x)+1 = x^2-4x+4#

Step 5. Express the right hand side as a square.

#f(x)+1= (x-2)^2#

Step 5. Isolate #f(x)#.

#f(x) = (x-2)^2-1#

The equation is now in vertex form.

#y = a(x – h)^2 + k#, where (#h, k#) is the vertex.

#h = 2# and #k = -1#, so the vertex is at (#2,-1#).

Graph