# What is the axis of symmetry and vertex for the graph x-4 = 1/4 (y+1)^2?

Jul 9, 2016

Vertex$\to \left(x , y\right) = \left(4 , - 1\right)$

Axis of symmetry is $y = - 1$

#### Explanation:

This is a quadratic in y. So instead of form$\text{ "y=ax^} + b x + c$ you have
$x = a {y}^{2} + b y + c$

Consequently it is still of general shape $\cup$ but is rotated ${90}^{0}$ clockwise to give $\subset$

Write the equation as:$\text{ } x = \frac{1}{4} \left(y + 1\right) + 4$

This equation format is in what is called 'Vertex Form'. With a slight adjustment you can read off the vertex coordinates directly from it

The $y$ is inside the bracket of $x = \frac{1}{4} \left(y + \textcolor{red}{1}\right) + \textcolor{b l u e}{4}$ so

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

${x}_{\text{vertex}} = \textcolor{b l u e}{4}$
This is taken directly from the equation without change

So Vertex$\to \left(x , y\right) = \left(4 , - 1\right)$