Express X2-16X+264 in the form (X+K)2+M

Question

I know the answer to this is X2-16X+264=(x-8)2+200  But do not no how to write it out please help. Both twos are squared. Thank you

Answer 1

Hi Roseland;

The vertex is (k,m).

In the equation of...

ax²+bx+c,

the x-value of the vertex is...

-b/2a

- {-16/[(2)(1)]}

8

The y-value of the vertex is...

X²-16X+264

8²-[(16)(8)]+264

64-128+264

200

Vertex is (8, 200)

(x-8)²+200

Let's check our results.

Let's FOIL (x-8)(x-8)...

FIRST...(x)(x)=x²

OUTER...(x)(-8)=-8x

INNER...(-80(x)=-8x

LAST...(-8)(-8)=64

x²-8x-8x+64

x²-16x+64

x²-16x+64+200

x²-16x+264

This is the original equation.