Question

Y = 2x^2 - 4x + 3 in vertex form

Answer 1

To convert the quadratic equation y = 2x^2 - 4x + 3 to vertex form, we can complete the square as follows:

y = 2x^2 - 4x + 3

y = 2(x^2 - 2x) + 3

y = 2(x^2 - 2x + 1 - 1) + 3 (adding and subtracting (2/2)^2 = 1 inside the parentheses)

y = 2((x-1)^2 - 1) + 3 (factoring the squared term)

y = 2(x-1)^2 - 2 + 3

y = 2(x-1)^2 + 1

Therefore, the vertex form of the quadratic equation y = 2x^2 - 4x + 3 is y = 2(x-1)^2 + 1, with vertex (1,1).