What is the axis y=x^2-5x-84 ?

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axis y=x^2-5x-84

axis

y = x^{2} - 5 x - 84

x = \frac{5}{2}

Solution steps

y = x^{2} - 5 x - 84

Rewrite

y = x^{2} - 5 x - 84

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{361}{4})) = (x - \frac{5}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{5}{2}, - \frac{361}{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{5}{2}

y = + \frac{1}{4} x^{2} + \frac{2}{3} x - \frac{1}{6}

x = + (y + 1)^{2} - 9

y = x^{2} - 3 x - 10

4 x = y^{2} - 4 y

3 x^{2} + 19 y = 0