SOLUTION: complete the square to find the equation of the parabola in the problem y=x²+6x+11

Question 1159736: complete the square to find the equation of the parabola in the problem y=x²+6x+11
Found 4 solutions by ankor@dixie-net.com, josgarithmetic, math_helper, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
complete the square to find the equation of the parabola in the problem
y = x² + 6x + 11
x^2 + 6x + __ = -11
to complete the square, half the coefficient of x and square it > 3^2
add 9 to both sides
x^2 + 6x + 9 = -11 + 9
Factor
(x+3)^2 = -2
The square root of both sides
x + 3 = +/-
extract the square root of -1 which is i
x + 3 = +/-
two solutions
x = -3 -
and
x = -3 +
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

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Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

This matches the form (axis of symmetry is parallel to y-axis)
where
focus is at (h, k+p)
directrix is at y = k-p
p=1/4, k=2, h=-3
focus at (-3,9/4)
directrix at y = 2-(1/4) = 7/4

Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.

On completing the square, see the lesson
    - HOW TO complete the square - Learning by examples
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Quadratic equations".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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Your request

"complete the square to find the equation of the parabola in the problem y=x²+6x+11."

sounds strange:   What you see in your post in front of you, is JUST an equation of a parabola.

So, if you want something special / (or different), then formulate it ADEQUATELY (!)

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