Question

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

Answer 1

Step-by-step explanation:

Please find the attachment of graph representing the axis of symmetry.

We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:

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

We can see that our function represents a parabola.

Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.

Let us find the vertex of our given parabola using formula: $x=\frac{-b}{2a}$, where,

a = Coefficient of $x^{2}.$

b = Coefficient of x.

To apply this formula we will represent our parabola as a quadratic equation $(ax^2+bx+c)$ as:

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

$f(x)=x^2-4x+5$  

Upon substituting a= 1 and b= -4 in the formula we will get,

$x=\frac{-(-4)}{2*1}$

$x=\frac{4}{2}$

$x=2$  

Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.

Answer 2

(x -2)^2 + 1 = 0
x^2 -4x + 5 = 0
The 'x' value of the axis of symmetry = 'x' value of the vertex.
To get this value, take the derivative of x^2 -4x + 5 = 0 which equals
2x -4 =0
x = 2 which equals the axis of symmetry