Question

Find the vertex for the following equation.
y = 2x^2 - 4x + 5

Answer 1

(1, 3)

Explanation:

`y = 2x^2 - 4x + 5\\\\y = 2(x^2 - 2x) + 5\\\\y=2(\underline{x^2-2\cdot x\cdot1+1^2}-1^2)+5\\\\y=2\big[(x-1)^2-1\big]+5\\\\y=2(x-1)^2-2+5\\\\y=2(x-1)^2+3\quad\implies\quad vertex:\ (1\,,\ 3)`