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

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axis y=(z-2)^2

axis

y = (z - 2)^{2}

z = 2

Solution steps

y = (z - 2)^{2}

Rewrite

y = (z - 2)^{2}

in the standard form:

4 \cdot \frac{1}{4} (y - 0) = (z - 2)^{2}

Therefore parabola properties are:

(h, k) = (0, 2), p = \frac{1}{4}

Parabola is of the form

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

and is symmetric around the

x

-axis

Axis of symmetry is a line parallel to the

x

-axis which intersects the vertex:

z = 2

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

y = + 2 x^{2} - x - 1

(y - 0)^{2} = 4 x - 4

y = 12 x (x - 4)

x - 2 = (y - 1)^{2}