What is the axis y=6(x-1/2)(x+3) ?

The axis y=6(x-1/2)(x+3) is x=-5/4

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axis y=6(x-1/2)(x+3)

axis

y = 6 (x - \frac{1}{2}) (x + 3)

x = - \frac{5}{4}

Solution steps

y = 6 (x - \frac{1}{2}) (x + 3)

Rewrite

y = 6 (x - \frac{1}{2}) (x + 3)

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{147}{8})) = (x - (- \frac{5}{4}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{5}{4}, - \frac{147}{8}), p = \frac{1}{24}

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{5}{4}

y = 9 x^{2} + 25

x^{2} - 4 x + 8 y - 12 = 0

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

6 y = x^{2} - 8 x + 14

y = - x^{2} - 8