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

Mar 6, 2016

Vertex$\to \left(x , y\right) \to \left(- 6 , - 4\right)$

Axis of symmetry$\to y = - 4$

#### Explanation:

Given: $\text{ } x = \frac{1}{4} {y}^{2} + 2 x - 2$

$\textcolor{b r o w n}{\text{This is just like the normal quadratic but as if it is }}$$\textcolor{b r o w n}{\text{rotated clockwise by } {90}^{o}}$

So let us treat it the same way!

Write as:$\text{ } x = \frac{1}{4} \left({y}^{2} + 8 y\right) - 2$

$\textcolor{b l u e}{\text{Axis if symmetry is at } y = \left(- \frac{1}{2}\right) \times \left(8\right) = - 4}$

Also $\textcolor{b l u e}{{y}_{\text{vertex}} = - 4}$

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By substitution

${x}_{\text{vertex}} = \frac{1}{4} {\left(- 4\right)}^{2} + 2 \left(- 4\right) - 2$

${x}_{\text{vertex}} = 4 - 8 - 2$

color(blue)(x_("vertex") =-6

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