Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y = 3x² + 6x + 2`?

Answer 1

AOS = -1
minimum = -1

Explanation:

Use the form `ax^2 +bx +c`, in your equation:

a = 3
b = 6
c = 2

Then the axis of symmetry (aos) is found using the formula:

`aos = (-b)/(2a)` or `(-6)/(2*3)= (-6)/6 = -1`

Okay now, if a is positive the function smiles and has a minimum, if a is negative the function frowns and has a maximum, In your case a = 3 and is positive so it smiles and has a minimum.

Finally, to find the maximum or minimum put the aos you found above back into the original function: `y = 3x^2 + 6x +2` and solve for y, THAT is your max or min:

`y = 3(-1)^2 + 6(-1) +2`
`y = 3 - 6 +2 = -1`

so the minimum is -1

As a side note the VERTEX is the (AOS, max/min) or (-1, -1) in your function.

graph{y=3x^2+6x+2 [-10, 10, -5, 5]}