What is the axis y=-x^2-6x-5 ?

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axis y=-x^2-6x-5

axis

y = - x^{2} - 6 x - 5

x = - 3

Solution steps

y = - x^{2} - 6 x - 5

Rewrite

y = - x^{2} - 6 x - 5

in the standard form

4 (- \frac{1}{4}) (y - 4) = (x - (- 3))^{2}

Therefore parabola properties are:

(h, k) = (- 3, 4), p = - \frac{1}{4}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = - 3

9 y^{2} - 6 y - 9 - x = 0

\frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 1

5 y^{2} - 2 x^{2} = 9

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

x^{2} - \frac{y ^{2}}{4} = 1