# How do you find the axis of symmetry, and the maximum or minimum value of the function  y=4(x+3)^2-4?

Mar 29, 2018

$\text{vertex } : \left(- 3 , - 4\right)$
$\text{minimum value } : - 4$

#### Explanation:

$y = a {\left(x - h\right)}^{2} + k$ is the Vertex Form of parabola,
$\text{Vertex } : \left(h , k\right)$

$y = 4 {\left(x + 3\right)}^{2} - 4$
$\text{Vertex } : \left(- 3 , - 4\right)$

The axis of symmetry intersects a parabola at its vertex.
$\text{axis of symmetry} : x = - 3$

$a = 4 > 0 \implies$ The parabola opens upward and has a minimum value at vertex:
The minimum value of y is -4.

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