What is the axis y=(x+1/2)(x-1/3) ?

The axis y=(x+1/2)(x-1/3) is x=-1/12

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axis y=(x+1/2)(x-1/3)

axis

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

x = - \frac{1}{12}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{25}{144})) = (x - (- \frac{1}{12}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{12}, - \frac{25}{144}), 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}{12}

y = (x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})

x^{2} = - 8 y

y^{2} + 4 x + 1 = 0

y = - \frac{1}{6} x^{2} + 4 x + 10

f (x) = - (x - 9)^{2} - 30