What is the axis y=x^2+7x+30 ?

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axis y=x^2+7x+30

axis

y = x^{2} + 7 x + 30

x = - \frac{7}{2}

Solution steps

y = x^{2} + 7 x + 30

Rewrite

y = x^{2} + 7 x + 30

in the standard form

4 \cdot \frac{1}{4} (y - \frac{71}{4}) = (x - (- \frac{7}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{7}{2}, \frac{71}{4}), 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 = - \frac{7}{2}

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

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

x = - 2 (y - 3)^{2} + 1

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

y = 5 x^{2} - 17 x + 1