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

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axis y=-x^2-x+6

axis

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

x = - \frac{1}{2}

Solution steps

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

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - \frac{25}{4}) = (x - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{2}, \frac{25}{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}

(x - 1)^{2} = - 20 (y - 4)

y = 4 x^{2} - 9

y = x^{2} - 20 x

y = x^{2} - 6 x + 13

x = (y + 3) (y - 1)