What is the axis y=x^2+18x+81 ?

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axis y=x^2+18x+81

axis

y = x^{2} + 18 x + 81

x = - 9

Solution steps

y = x^{2} + 18 x + 81

Rewrite

y = x^{2} + 18 x + 81

in the standard form

4 \cdot \frac{1}{4} (y - 0) = (x - (- 9))^{2}

Therefore parabola properties are:

(h, k) = (- 9, 0), 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 = (2 x + 1) (4 - 9 x) - 2 x (3 x + 11)

y = 16 x - 4 x^{2}

y = 4 x^{2} + 6

y = \frac{x ^{2} - 2 x - 19}{5}

y = x^{2} + 8 x - 1