Question

Put the equation y=X^2+12x+32 in the form y=(x+h)^2+k

Answer 1

Given equation

y = x^2+12*x + 32

We have to write the equation in the form -----> y = ( x + h )^2 + k

This form is called the vertex form

x^2+12*x + 32 = x^2 + 2*6*x + 6^2 - 6^2 + 32

=> x^2 + 2*6*x + 6^2 - 6^2 + 32 = ( x + 6 )^2 - 6^2 + 32

=> ( x + 6 )^2 - 6^2 + 32 = ( x + 6 )^2 - 36 + 32

=> ( x + 6 )^2 - 36 + 32 =  ( x + 6 )^2 - 4

=> ( x + 6 )^2 - 4 = ( x + 6 )^2 + ( - 4 )

So , y = ( x + 6 )^2 + ( - 4 ) which is in the form  y = ( x + h )^2 + k