What is the axis y=x^2-6x+13 ?

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axis y=x^2-6x+13

axis

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

x = 3

Solution steps

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

Rewrite

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

in the standard form

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

Therefore parabola properties are:

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

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 = 3

x = (y + 3) (y - 1)

y^{2} = 4 \cdot 3 x - 6

x^{2} - 10 x - 24 y = - 25 - 24

y \geq x^{2} - 9

y = 4 - 5 x^{2}