Rewrite the quadratic equation y=x^2-8x+19 in vertex form

Question

Rewrite the quadratic equation y=x^2-8x+19 in vertex form

 

Answer 1

y = x² - 8x + 19  

y = (x² - 8x + c)+19 - c      You need to find c by completing the square.  c = (b/2)² = (-8/2)² = (-4)² = 16

y = (x² -8x + 16) + 19-16   Add c to the parenthesis and subtract from the constant.

y = (x - 4)(x-4) + 3            Factor the trinomial and combine the constants.

y = (x-4)² + 3                    Vertex Form of the equation.  The vertex is (4, 3).