What is the axis y=x^2+6x+9 ?

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axis y=x^2+6x+9

axis

y = x^{2} + 6 x + 9

x = - 3

Solution steps

y = x^{2} + 6 x + 9

Rewrite

y = x^{2} + 6 x + 9

in the standard form

4 \cdot \frac{1}{4} (y - 0) = (x - (- 3))^{2}

Therefore parabola properties are:

(h, k) = (- 3, 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 = - 3

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

y = x^{2} - x - 2

y = - 2 x^{2} - 3

x = \frac{1}{8} y^{2}

y = x^{2} + 19 x + 60