What is the axis y=+x^2+4x+7 ?

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axis y=+x^2+4x+7

axis

y = + x^{2} + 4 x + 7

x = - 2

Solution steps

y = x^{2} + 4 x + 7

Rewrite

y = x^{2} + 4 x + 7

in the standard form

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

Therefore parabola properties are:

(h, k) = (- 2, 3), 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 = - 2

y^{2} = 40 x

y = - x^{2} + 64 x - 292

y = - 45 x^{2} - 27 x + 2

y = - \frac{1}{2} (x - 3)^{2} - 8

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