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

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axis y=-1+3x+x^2

axis

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

x = - \frac{3}{2}

Solution steps

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

Rewrite

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

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 = 7 x^{2} - 5 x + 9

y = (x + 2)^{2}

y = - 20 x^{2} + 20000 x - 1800000

(x + 4)^{2} = - 6 (y - 3)

y = x^{2} - 4 x + 7