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 = x^{2} - 4 x + 2

(x - 4)^{2} = 20 (y + 5)

y = (x + 9) (x + 8)

y^{2} + 12 x - 2 y - 11 = 0

(x + 3)^{2} = 12 y