vertices -x^2

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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Steps Examples

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directrix y=2x²−1+5x−6

Solution

y=−414

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Solution steps

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Parabola Directrix

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(y−k)=(x−h)² is the standard equation for an up-down facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite y=2x²−1+5x−6 in the standard form

4· 18 (y−(−818 ))=(x−(−54 ))²

(h, k)=(−54 , −818 ), p=18

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance −p from the center (−54 , −818 ) y-coordinate

y=−818 −p

y=−818 −18

Refine

y=−414

Description

The Limit Calculator is an essential online tool designed to compute limits of functions efficiently. Here's how to use it:

Begin by entering the mathematical function for which you want to compute the limit into the above input field, or scanning the problem with your camera.
Choose the approach to the limit (e.g., from the left, from the right, or two-sided).
Input the point at which you want to evaluate the limit.
Once you've entered the function, selected the approach, and specified the limit point, click the 'Go' button to generate the result.

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