What is the axis y=x^2+x+5 ?

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axis y=x^2+x+5

axis

y = x^{2} + x + 5

x = - \frac{1}{2}

Solution steps

y = x^{2} + x + 5

Rewrite

y = x^{2} + x + 5

in the standard form

4 \cdot \frac{1}{4} (y - \frac{19}{4}) = (x - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{2}, \frac{19}{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{1}{2}

y = 6 x^{2} + 7 x - 3

y = 8 - 2 x^{2}

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

y = (x - 3) (x - 7)

- 2 x^{2} + 24 x + y - 70 = 0