Express f (x) = x2 – 6x + 14 in the form f (x) = (x – h)2 + k, where h and k are to be determined.

Question

amistre64 · Answer

also known as completing the square

amistre64 · Answer

we want to add zero to this thing so that the form changes, but the value remains the same

what is half of that middle term?

anonymous · Answer

-3x

amistre64 · Answer

good, lets ignore that "x" tagged on

(x-3)^2 is going to be in our setup

since -3*-3 = 9  , we have to adjust this thing by adding 9-9 to it

amistre64 · Answer

x2 – 6x + (9 - 9) + 14  ; just adding zero

(x2 – 6x + 9) - 9 + 14

(x-3)^2 - 9 + 14, now we combine the last amounts and we are in the form you want

anonymous · Answer

so (x-3)^2+5

amistre64 · Answer

correct, the key is in knowing that "completing the square" routine

anonymous · Answer

okay thank you! your better at explaining this than my teacher

amistre64 · Answer

good luck ;)