What are the vertex, focus and directrix of $y=(x + 6)^2/36+3$ ?

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Answer 1 · 2017-11-07T23:25:12

Given: $y=(x + 6)^2/36+3$

The vertex form is:

$y = 1/(4f)(x - h)^2 + k$

Writing the given equation in that form:

$y=1/36(x - (-6))^2+3$

Matching terms and factors:

$4f = 36$

$f = 9$

$h = -6$

$k = 3$

The vertex is:

$(h,k)$

$(-6,3)$

The focus is

$(h,k+f)$

$(-6,3+9$

$(-6,12)$

The directrix is:

$y = k-f$

$y = 3 - 9$

$y = -6$

What are the vertex, focus and directrix of y=(x + 6)^2/36+3 y=(x + 6)^2/36+3 ?