Respuesta :

kudzordzifrancis
ANSWER

The vertex form is

[tex]y = 3 {(x + 1)}^{2} + 5[/tex]

EXPLANATION

We want to write

[tex]y = 3 {x}^{2} + 6x + 8[/tex]
in the vertex form which of the form


[tex]y = a {(x - h)}^{2} + k[/tex]

We achieve this BG completing the square.

We proceed as follows,

[tex]y = 3( {x}^{2} + 2x) + 8[/tex]


We add and subtract half the coefficient of x multiplied by a factor of 3 which is
[tex]3( \frac{1}{2} \times 2)^{2} = 3( {1)}^{2} [/tex]


This gives us,


[tex]y = 3( {x}^{2} + 2x) + 3 {(1)}^{2} -3 {(1)}^{2} + 8[/tex]

We still factor 3 out of the first two terms to get,

[tex]y = 3( {x}^{2} + 2x + {1}^{2} ) -3 {(1)}^{2} + 8[/tex]

We now got a perfect square, which factors to,


[tex]y = 3 {(x + 1)}^{2} + 5[/tex]
The equation is now in the vertex form.

Otras preguntas