What is the axis y=x^2-x-20 ?

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axis y=x^2-x-20

axis

y = x^{2} - x - 20

x = \frac{1}{2}

Solution steps

y = x^{2} - x - 20

Rewrite

y = x^{2} - x - 20

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{81}{4})) = (x - \frac{1}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{2}, - \frac{81}{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^{2} + y = 5

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

y = 1 - x^{2}

y = 2 x^{2} - 1 - (5 x - 6)

y = 2 (x + 1)^{2}