Question

The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry?

Answer 1

First, simplify the expression of the function $f(x)=x^2-4x+6$ highlighting the perfect square:

$f(x)=x^2-4x+4-4+6=(x-2)^2+2.$

Then find the vertwx of parabola. When x=2, f(2)=2 and the coordinates of the vertex are (2,2). The axis of symmetry passes through the vertex and is parallel to the y-axis. Therefore, its equation is x=2 (see attached graph for details).

Answer: x=2.