What is the axis y=x^2-x+5 ?

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axis y=x^2-x+5

axis

y = x^{2} - x + 5

x = \frac{1}{2}

Solution steps

y = x^{2} - x + 5

Rewrite

y = x^{2} - x + 5

in the standard form

4 \cdot \frac{1}{4} (y - \frac{19}{4}) = (x - \frac{1}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{2}, \frac{19}{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}

y = x^{2} - 12 x + 46

18 x^{2} - 64 x - 14 y + 150 = 0

y = x^{2} + 4

y^{2} = 8 x

y^{2} = 20 x