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

y=x²+4x+11

y = (x²+2 (2) (x) + 2²) + 11-2²

y = (x+2) ²+7