What is the axis y=-x^2+18x-82 ?

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axis y=-x^2+18x-82

axis

y = - x^{2} + 18 x - 82

x = 9

Solution steps

y = - x^{2} + 18 x - 82

Rewrite

y = - x^{2} + 18 x - 82

in the standard form

4 (- \frac{1}{4}) (y - (- 1)) = (x - 9)^{2}

Therefore parabola properties are:

(h, k) = (9, - 1), 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 = 9

(y + 4)^{2} = 4 (x + 1)

x^{2} + 8 y = 0

y = x^{2} + 12 x + 28

y = 6 x^{2} - 4

y = 3 x^{2} + 15 x