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

May 19, 2018

AOS = -1
minimum = -1

#### Explanation:

Use the form $a {x}^{2} + b x + c$, in your equation:

a = 3
b = 6
c = 2

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

$a o s = \frac{- b}{2 a}$ or $\frac{- 6}{2 \cdot 3} = \frac{- 6}{6} = - 1$

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: $y = 3 {x}^{2} + 6 x + 2$ and solve for y, THAT is your max or min:

$y = 3 {\left(- 1\right)}^{2} + 6 \left(- 1\right) + 2$
$y = 3 - 6 + 2 = - 1$

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]}