Question

Rewrite equation in vertex form y=x^2+4x+2

Answer 1

Answer: $y =(x+2)^2-2$

Steps:

The general vertex form of a parabola is as follows:

$y = a(x-x_v)^2+b$

where xv is the x coordinate of the vertex, a is the coefficient determining how wide/narrow the parabola is and whether it is open-up (+) or open-down (-), and b is the bias (vertical shift.

Transforming an expression into the vertex form involves completing the square step:

$y=x^2+4x+2\\y = x^2 + 2\cdot2 x+ 2 + 4 - 4= (x+2)^2-2\\y =(x+2)^2-2\\\implies x_v = -2,a=1, b=-2$