Question

Write 3x2 + 12x - 1 = 0 in vertex form

Answer 1

@ganeshie8

Answer 2

do you know what a "perfect square trinomial" is?

Answer 3

yes @jdoe0001

Answer 4

so let us group that first then \(\bf 3x^2 + 12x - 1 = 0\implies (3x^2 + 12x) - 1 = 0\implies 3(x^2+4x)-1=0
\\ \quad \\
3(x^2+4x+{\color{red}{ \square }}^2)-1=0\)

so... what do you think we need there to get a "perfect square trinomial" in the parentheses?

Answer 5

Vertex form is: f(x) = a(x - h)^2 + k,

(3x^2 + 12x) - 1 = 0

3(x^2 + 4x) - 1 = 0

3(x^2 + 4x + 4) - 1 - 12 = 0 ... you added 3(4) to the equation, to keep it balanced you subtract 12, 3 * 4 = 12. -1 - 12 = -13

f(x) = 3(x + 2)^2 - 13