What is the axis y= 1/2 x^2+2 ?

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axis y= 1/2 x^2+2

axis

y = \frac{1}{2} x^{2} + 2

x = 0

Solution steps

y = \frac{1}{2} x^{2} + 2

Rewrite

y = \frac{1}{2} x^{2} + 2

in the standard form:

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

Therefore parabola properties are:

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

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 = 0

y = 2 x^{2} - 12 x + 22

y = - 2 x^{2} + 3 x

x^{2} = 8 (y - 3)

(x - 2)^{2} = 40 (y - 2)

y = 6 x^{2} - 13 x + 6