The standard form of the equation of a parabola is y=x^2 + 4x + 11. what is the vertex form of the equation?

y = (x + 2)² + 7

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

add/ subtract (half the coefficient of the x term )²

y = x² + 4x + (2)² - (2)² + 11

  = x² + 4x + 4 - 4 + 11

  = (x + 2)² + 7 ← in vertex form

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.