First, factor out the 2 from the x terms:
Next, take half the coefficient of x, , square it, , and add it to complete the perfect square trinomial in parentheses. But, you really added twice that amount since we have a factor of outside the parentheses. So, to keep things balanced in the equation, we must subtract twice that amount, , outside the parentheses. 'What one addeth to just one side of an equation, one must taketh away'.
The minimum point is the y-coordinate of the vertex:
The y-intercept can be found from the original function by setting x=0 and solving for y.
The x-intercepts (zeros of the function) are found by setting the original quadratic = 0 and use the quadratic formula to find the values for x.