What is the axis x=-1/2 (y+4)^2-5 ?

The axis x=-1/2 (y+4)^2-5 is y=-4

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axis x=-1/2 (y+4)^2-5

axis

x = - \frac{1}{2} (y + 4)^{2} - 5

y = - 4

Solution steps

x = - \frac{1}{2} (y + 4)^{2} - 5

Rewrite

x = - \frac{1}{2} (y + 4)^{2} - 5

in the standard form:

4 (- \frac{1}{2}) (x - (- 5)) = (y - (- 4))^{2}

Therefore parabola properties are:

(h, k) = (- 5, - 4), p = - \frac{1}{2}

Parabola is of the form

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

and is symmetric around the

x

-axis

Axis of symmetry is a line parallel to the

x

-axis which intersects the vertex:

y = - 4

(y - 2)^{2} = - (x + 4)

y = 3 (x - 1) (x + 2)

x^{2} + 8 x + 12

y = 2 (x + 3)^{2} + 4

f (x) = - 3 x^{2} + 5 x - 2