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 +
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
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