Question

K(x) = {x2 - 4x + 10 What is the line of symmetry ?

Answer 1

Using completing the square method

`\begin{gathered} x^2\text{ }-4x\text{ + 10 = 0} \\ \\ x^2\text{ - 4x = -10} \\ \\ \text{Add the square of half the coefficient of x to both sides} \\ \\ x^2-4x+2^2=-10+2^2 \\ (x-2)^2\text{ = -10 + 4} \\ (x-2)^2\text{ = -6} \\ \\ (x-2)^2\text{ + 6 = 0} \end{gathered}`

The line of symmetry at h from the coordinate of the vertex (h,k)

The vertex is (2, 6)

where h = 2

Thus, the line of symmetry is at 2