Find parabola given the vertex (-3, 1)

The calculator will find the equation of a parabola and its properties given the vertex $$$\left(-3, 1\right)$$$, with steps shown.

Type:

Vertex:$$$($$$

,

$$$)$$$

Focus:$$$($$$

,

$$$)$$$

Directrix:

First point:$$$($$$

,

$$$)$$$

Second point:$$$($$$

,

$$$)$$$

Third point:$$$($$$

,

$$$)$$$

Axis/direction:

Vertical axis means parallel to the y-axis, horizontal axis means parallel to the x-axis.

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Your Input

Find the equation, vertex, focus, directrix, axis of symmetry, latus rectum, length of the latus rectum (focal width), focal parameter, focal length, eccentricity, x-intercepts, y-intercepts, domain, and range of the parabola found from the given data: the vertex $$$\left(-3, 1\right)$$$.

Solution

The equation of a parabola is $$$y = \frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k$$$, where $$$\left(h, k\right)$$$ is the vertex and $$$\left(h, f\right)$$$ is the focus.

Thus, $$$h = -3$$$, $$$k = 1$$$.

We need 3 equations to find a parabola. Since we don't have these, the parabola can't be found.

Answer

Not enough data to build a parabola.

Find parabola given the vertex $$$\left(-3, 1\right)$$$

Your Input

Solution

Answer