What is the axis y=x^2+2x+1 ?

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axis y=x^2+2x+1

axis

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

x = - 1

Solution steps

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

Rewrite

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

in the standard form

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

Therefore parabola properties are:

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

y = - x^{2} - 2 x + 7

y = 2 x^{2} - 7

(x + 1)^{2} = 12 y

x = 2 (y - 5)^{2} + 3

x^{2} + 10 x = - 12 y - 1