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$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center, $a$ is the semi-major axis, and $b$ is the semi-minor axis.

$y=ax^2+bx+c$, where the graph is a U-shaped curve that may open upwards or downwards.

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $a>b$ and $(h,k)$ is the center.

$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$, where $a>b$ and $(h,k)$ is the center.

$x=ay^2+by+c$, where the parabola opens to the left or right.

$(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center, $a$ is the distance to the vertices along the transverse axis, and $b$ is the distance to the vertices along the conjugate axis.