If you have a parametric equation grapher, graph the equations over the given intervals. Parabol

step 1 Okay, so now we will solve the problem. We will draw the wrap of the parabola x equal to t plus

If you have a parametric equation grapher, graph the...

Key Concepts

Parametric Equations

Parametric equations describe a curve by expressing the coordinates as functions of an independent parameter, usually denoted as t. This method allows more flexibility in representing curves, especially when the relationship between x and y is not a simple function, as both coordinates are defined separately in terms of t.

Parameter Intervals

The parameter interval defines the range of values that the parameter can take. This range is crucial because it dictates which portion of the parametric curve is graphed, ensuring that the plot is accurate and complete only for the section of the curve corresponding to the specified t-values.

Graphing Parametric Curves

Graphing parametric curves involves computing points by substituting different values from the parameter interval into the parametric equations to obtain corresponding x and y coordinates. This collection of points is then plotted on the coordinate plane to form the curve. Using a parametric equation grapher automates this process, making it easier to visualize the curve over the given range.

Transcript

00:05 Okay, so now we will solve the problem.

00:08 We will draw the wrap of the parabola x equal to t plus 3 and y equal t squared minus 1 and the limitation of the t will be from negative 2 from 2 and this is my solution.

00:25 So the first one we have x equal to t plus 3 so we can do conversion we will have that the t will be equal x minus 3 and then divide by 2 and then we will be substitute t to the equation of the y so we will have like y equal t square minus 1 right but like t equal x minus 3 on the top and divide by 2 on the bottom so the y will be equal x minus 3 divide by 2 and 2 and square total square and minus 1 and then we will be factor this equation so you may be remember about equation like a minus b total square will be equal a square minus two a b plus b square square so so this is like the remember equation we will have to remember like a minus b total square will be equal a square minus 2 ab and plus to b square so when we apply this equation in here so we will have like x square minus divided by 4 minus 3 x because like we have 2 ab right so 2 times 1 over 2 and 1 time 3 will be equal 3 x and then like 3 over 2 will be total square up we will have like 9 over 4 and then we have negative 1 from here we just rewrite from here and then we will reduce this equation so x squared divide by 4 we keep them and then we just rewrite them 3 square uh 3 x we just rewrite them and then 9 over 4 minus 1 this just if we we do have the same bottom so like this so 9 over 4 minus 4 over 4 so we will have 9 minus 4 on the top and then the bottom will be the 4 so this is the basic skill for the fraction minus so we will have 5 over 4 okay, so from the y equal this equation and then we reduce them to make them shorter.

03:44 So y will be equal 1 over 4 x squared minus 3 x and plus 5 over 4.

03:56 Okay, sorry my...

04:04 Okay, so and then we will be find the value.

04:09 So we will find the value of the...

04:12 I will make them higher so we can see this.

04:16 Okay, so from this equation, okay, this equation, okay, i will erase this so a little bit mess up in here.

04:37 This is a new technical, so i try to learn them, so hopefully, okay, and we do another one.

04:53 My wrap is so ugly.

04:56 Okay, so before i move this i will re - undo everything.

05:06 So hopefully, okay, okay, it's better.

05:26 Okay, a little bit mess up in here, but it's okay...