Question

Complete the square to rewrite y= x2 - 8x+ 15 in vertex form. Then state

whether the vertex is a maximum or a minimum and give its coordinates.

Answer 1

there's a minimum at (4, -1)

Explanation:

Please use " ^ " to denote exponentiation: y= x^2 - 8x+ 15.

To "complete the square," take half of the coefficient of x (which is -8). Square this result, obtaining 16.

In y= x^2 - 8x+ 15, add 16, and then subtract 16, between -8x and +15:

y = x^2 - 8x + 16 - 16 + 15

This becomes:

y = (x - 4)^2 -1

Reading off the coordinates of the vertex, we get (4, -1). Because the coefficient of the (x - 4)^2 term is positive, we know .there's a minimum at (4, -1)