Question

Write x2 - 2x + 5 = 0 in vertex form. (Be sure to write your response in the form a(x-h)^2+k=0 with no spaces!)

Answer 1

To write the given quadratic equation to its vertex form, we first form a perfect square.

x² - 2x + 5 = 0
Transpose the constant to other side of the equation,
x² - 2x = -5
Complete the square in the left side of the equation,
x² - 2x + (-2/1(2))² = -5 + (-2/1(2))²
Performed the operation,
x² - 2x + 1 = -5 + 1
Factor the left side of the equation,
(x - 1)² = -4

Thus, the vertex form of the equation is,
(x-1)² + 4 = 0