# How do you find the vertex and intercepts for ( y - 2)^2 = 4(x - 1)?

Dec 22, 2015

This is the equation for a parabola that opens horizontally instead of vertically so the standard formulae can be used.

#### Explanation:

This is the equation for a parabola that opens horizontally instead of vertically. First expand the expression to get it into standard parabola form.
${y}^{2} - 4 y + 4 = 4 x - 4$
$4 x = {y}^{2} - 4 y + 8$
$x = {y}^{2} / 4 - y + 2$
$x = {\left(\frac{y}{2} - 1\right)}^{2}$
The vertex is the minimum value of the expression so is $\left(0 , 2\right)$
The y intercept ( $x = 0$) is the same as the vertex.
The x intercept ($y = 0$) is $\left(1 , 0\right)$