Question

What are the solutions to the following system of equations? y = x^2 - 3x + 3

Answer 1

x = 3/2 + root(3)/2 or x = 3/2 - root(3)/2

In vertex form the equation is y = (x - 3/2)^2 + 3/4

Explanation:

y = x^2 - 3x + 3

y = x^2 - 3x + 9/4 - 9/4 + 3

y = (x - 3/2)^2 + 3/4

I think you want to find the roots to the equation, right?

so

y = (x - 3/2)^2 + 3/4 = 0

(x - 3/2)^2 = -3/4

x - 3/2 = root(-3/4)

x = 3/2 + root(3)/2 or x = 3/2 - root(3)/2