What is the axis y=x^2+3x-1 ?

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axis y=x^2+3x-1

axis

y = x^{2} + 3 x - 1

x = - \frac{3}{2}

Solution steps

y = x^{2} + 3 x - 1

Rewrite

y = x^{2} + 3 x - 1

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{13}{4})) = (x - (- \frac{3}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{3}{2}, - \frac{13}{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{3}{2}

y^{2} = - 36 x

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

y = + x^{2} + 81

y = - \frac{1}{16} (x - 1)^{2} - 1

y = x^{2} + 7 x + 30