Question

Complete the square to rewrite y = x^2 - 6x + 14 in vortex form. Then state whether the vertex is a maximum or minimum and give its coordinates

Answer 1

To complete the square, we need to add and subtract the square of half of the coefficient of x:
y = x^2 - 6x + 14
y = (x^2 - 6x + 9) + 14 - 9
y = (x - 3)^2 + 5


hope this helps!

Therefore, the vertex form of the equation is y = (x - 3)^2 + 5, where the vertex is at (3, 5). Since the coefficient of the x^2 term is positive, the parabola opens upwards and the vertex represents the minimum point of the parabola. Thus, the vertex is a minimum and its coordinates are (3, 5).