# How do you tell whether the graph opens up or down, find the vertex and the axis of symmetry of y=3(x+4)^2-2?

Aug 26, 2017

See below.

#### Explanation:

When a quadratic is arranged in the form $a {\left(x - h\right)}^{2} + k$
$k$ is the minimum or maximum of the function.
$h$ is the axis of symmetry.
From example:

vertex is $\left(- 4 , - 2\right)$
axis of symmetry is $- 4$

If $a$ is negative, then the parabola is inverted i.e. $\bigcap$

If $a$ is positive, then the parabola $\bigcup$

Aug 30, 2017

As the ${x}^{2}$ term is positive the graph opens upwards

Vertex $\to \left(x , y\right) = \left(- 4 , - 2\right)$

So axis of symmetry is $x = - 4$

#### Explanation:

If you expand the brackets and multiply by the three the first term is

$+ 3 {x}^{2}$

As this is positive the graph is of general shape $\cup$

Suppose it had been negative then in that case the graph would be of form $\cap$

The given equation format is of type 'completing the square' also known as 'vertex form'.

$y = 3 {\left(x + \textcolor{red}{4}\right)}^{2} \textcolor{b l u e}{- 2}$

${x}_{\text{vertex}} = \left(- 1\right) \times \textcolor{red}{4} = - 4$

${y}_{\text{vertex}} = \textcolor{b l u e}{- 2}$

Vertex $\to \left(x , y\right) = \left(- 4 , - 2\right)$