Question

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

Answer 1

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 - 4y +4 = 4x - 4`
`4x = y^2 -4y +8`
`x = y^2/4 - y +2`
`x = (y/2 - 1)^2`
The vertex is the minimum value of the expression so is `(0,2)`
The y intercept ( `x=0`) is the same as the vertex.
The x intercept (`y=0`) is `(1,0)`