What is the axis y=x^2-26x+65 ?

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axis y=x^2-26x+65

axis

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

x = 13

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- 104)) = (x - 13)^{2}

Therefore parabola properties are:

(h, k) = (13, - 104), 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 = 13

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

x^{2} - x + 5

y = 2 (x - 9)^{2}