What is the axis y=3x^2+15x ?

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axis y=3x^2+15x

axis

y = 3 x^{2} + 15 x

x = - \frac{5}{2}

Solution steps

y = 3 x^{2} + 15 x

Rewrite

y = 3 x^{2} + 15 x

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{75}{4})) = (x - (- \frac{5}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{5}{2}, - \frac{75}{4}), p = \frac{1}{12}

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 = - 2 x^{2} + 11

x^{2} - 4 x - 8 y + 12 = 0

y = x^{2} + 10 x

x = (- 20 y + 13)^{2}

(x - 3)^{2} = 12 (y - 1)