Write Y=3x^2+6x+7 in vertex form

Question

asked Oct 28, 2024 152k views

1 Answer

Treena · Answer 1 · 2024-11-02T19:28:26+0000

Answer:
$3(x+1)^(2) +4\\$

Explanation:

$3x^(2) +6x+7\\$ leave space to complete the square

$3x^(2) +6x\\$ + 7 factor out a 3 from the first part

3(x^(2) +2x ) + 7 complete the square by dividing middle number by 2 and squaring

(2)/(2) ^(2) = 1 1 is your completion of square

$3(x^(2) +2x+1)+7-3\\$ you need to balance the+1 but the 3 in front means you actually added 3 so you need to balance by subtracting3

$3(x+1)^(2) +4\\$ factor gives you this simplified form which is vertex form