What is the axis y=ax^2 ?

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axis y=ax^2

axis

y = a x^{2}

x = 0

Solution steps

y = a x^{2}

Rewrite

y = a x^{2}

in the standard form:

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

Therefore parabola properties are:

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

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 = + x^{2} + 3 x - 4

y = x^{2} + 8 x + 15

y = (2 x - 1) (5 x - 6)

y = 1 - x - x^{2}

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