Question

Which equation represents y = x2 + 12x + 27 in vertex form?


y = (x + 6)2 − 9


y = (x + 6)2 + 21


y = (x + 6)2 + 9


y = (x + 6)2 + 27

Answer 1

Do you know how to complete a square?

Answer 2

I've heard of it, never used it in practice

Answer 3

There are two ways:
1. Complete a square
2. Open parenthesis, simplify and compare

Answer 4

Can you do that?

Answer 5

i can try, let me do that

Answer 6

How are you, need help?

Answer 7

ok would it be the last option because the product of the roots (-9,-3?) is 27?

Answer 8

Apply
(a + b)^2 = a^2 + 2ab + b^2
to
(x + 6)^2
What you get?

Answer 9

Replace a with x and b with 6.
What is (x + 6)^2 = ...

Answer 10

(x + 6)^2= x^2 + 2x6 + 6^2
how would i do the 2x6 part?

Answer 11

2 times 6 is ... and 6 times 6 is ...

Answer 12

12 and 36.. i still don't understand where this is all going..?

Answer 13

(x + 6)^2= x^2 + 12x + 36
Now subtract 9 for the first option, what you get?

Answer 14

how did we get to subtracting 9? and subtract it from which number(s)

Answer 15

y = (x + 6)^2 − 9 opened the parenthesis and got:
y = x^2 + 12x + 36 - 9
Can you simplify?

Answer 16

x^2+12x+27

Answer 17

Now you need to compare this with the given, are they same or different?

Answer 18

different..

Answer 19

They are same and this option is your answer ...
(x^2 and x2 is same in terms of your question)

Answer 20

ok ok so it would be the first option right? that is the on that is showing the same thing that we just did

Answer 21

thank you so much!

Answer 22

No problem