Question

How do you write the Vertex form equation of the parabola `y=x^2+4x+1`?

Answer 1

# y = (x+2)^2 - 3

Explanation:

the standard form of a quadratic is `y = ax^2 + bx + c`

the equation here `y = x^2 + 4x + 1`

gives by comparison : a = 1 , b =4 and c = 1

the vertex form of the equation is

`y =a (x - h )^2 + k`

where (h , k ) are the coords of the vertex.

x-coord of vertex = `-b/(2a) = -4/2 = -2`

and y-coord `= (-2)^2 +4(-2) + 1 = 4 - 8 + 1 = -3`

hence (h , k) = ( -2 , -3 ) and a = 1

equation in vertex form is : `y = (x + 2)^2 - 3`