What is the axis y=-1/2 x^2-5x-15/2 ?

The axis y=-1/2 x^2-5x-15/2 is x=-5

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axis y=-1/2 x^2-5x-15/2

axis

y = - \frac{1}{2} x^{2} - 5 x - \frac{15}{2}

x = - 5

Solution steps

y = - \frac{1}{2} x^{2} - 5 x - \frac{15}{2}

Rewrite

y = - \frac{1}{2} x^{2} - 5 x - \frac{15}{2}

in the standard form

4 (- \frac{1}{2}) (y - 5) = (x - (- 5))^{2}

Therefore parabola properties are:

(h, k) = (- 5, 5), p = - \frac{1}{2}

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 = - 5

x = y - y^{2}

y = x^{2} - 5 x

y = 600 - 10 x + 0.25 x^{2}

y = - 0.00004 x^{2} - 0.00105 x + 1.055

(x + 3)^{2} = 5 y - 8