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

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axis y=-x^2+5x-2

axis

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

x = \frac{5}{2}

Solution steps

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

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - \frac{17}{4}) = (x - \frac{5}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{5}{2}, \frac{17}{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

y = x^{2} - 20 x + 100

y = x^{2} - 14 x + 48

y = (2 x + 5)^{2}

y = - 1.25 x^{2} + 50 x + 4000