Question

What is the axis of symmetry? What are the coordinates of the vertex?
y = 3x² +6x-2

Answer 1

Explanation:

the general equation of a parabola in a "y = ..." orientation is

y = a(x – h)² + k

where (h, k) is the vertex.

the axis of symmetry is

x = h

and for the form

y = ax²+ bx + c

this means

x = - b/(2a)

we have here

y = 3x² + 6x - 2

so we get the axis of symmetry directly :

x = -6/(2×3) = -6/6 = -1

x = -1

and we know x = h.

so we have

y = 3(x + 1)² + k = 3(x² + 2x + 1) + k =

= 3x² + 6x + 3 + k

comparing it to our original equation we see

3 + k = -2

k = -5

so, the vertex is

(-1, -5)