What is the axis x=-(y-2)^2-3 ?

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axis x=-(y-2)^2-3

axis

x = - (y - 2)^{2} - 3

y = 2

Solution steps

x = - (y - 2)^{2} - 3

Rewrite

x = - (y - 2)^{2} - 3

in the standard form:

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

Therefore parabola properties are:

(h, k) = (- 3, 2), p = - \frac{1}{4}

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 = 2

y = x^{2} - 2 x

y = (x + 5) (x + 3)

y^{2} = - 24 x

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

- 4 y^{2} - 12 y + 1 = 3 x - 5