What is the axis (y-2)^2=3(x-5) ?

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axis (y-2)^2=3(x-5)

axis

(y - 2)^{2} = 3 (x - 5)

y = 2

Solution steps

(y - 2)^{2} = 3 (x - 5)

Rewrite

(y - 2)^{2} = 3 (x - 5)

in the standard form:

4 \cdot \frac{3}{4} (x - 5) = (y - 2)^{2}

Therefore parabola properties are:

(h, k) = (5, 2), p = \frac{3}{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 = 0.5 (x + 1)^{2} - 2

y = x^{2} - 26 x + 65

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

y = - 2 x^{2} + 5 x - 6

y^{2} - 3 y - x + 3 = 0