{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-572d6a42.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-f4d0de30.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Master finding the focus and directrix of a parabola with vertex at the center' data-url='/boclips/videos/636737d2dc85e4451bc6fef7' data-video-url='/boclips/videos/636737d2dc85e4451bc6fef7' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nMaster finding the focus and directrix of a parabola with vertex at the center\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30355462\" href=\"/search?publisher_ids%5B%5D=30355462\"\u003eBrian McLogan\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eSo just like we did in the last video where we wanted to determine the opening, does a graph open up, down, left, or right, that's going to be the first thing we're going to want to do in these problems as well. So, and again, that's all...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eSo just like we did in the last video where we wanted to determine the opening, does a graph open up, down, left, or right, that's going to be the first thing we're going to want to do in these problems as well. \u003cbr/\u003e\u003cbr/\u003eSo, and again, that's all going to hinge on what variable is being squared. So you can see we have two conic sections [INAUDIBLE] here-- one, where the x is squared, and then one where the y squared. Well, when the x is squared, just like quadratics, the graph is going to open up or down. And for the y squared that means the graph is going to open up to the right or to the left. So, and the first thing we want to do for all of these videos, I want to look at which variable is going to be squared. \u003cbr/\u003e\u003cbr/\u003eSo obviously, if I expanded x minus 2 squared and I expand it out, I would have x as squared. So that means this graph is going to be opening up or it's going to be opening down. OK? \u003cbr/\u003e\u003cbr/\u003eNow, in the previous examples, we didn't have an h and a k and we just had do, you know the vertex was at 0, 0. And that was fine, and that kind of made it helpful and easy to find the vertex-- or the focus and the directrix. But now, we have some x plus and x minus, y plus and y minus. And what that represents is our h and our k, which is going to represent the vertex of our parabola. Remember the vertex of the parabola is going to be your absolute min or max of the point. It's where it kind of that line of symmetry goes through your vertex. \u003cbr/\u003e\u003cbr/\u003eSo that's going to be the first thing we're going to want to identify. So remember, notice in the equation, kind of like when we first started doing vertex form of quadratics. It's x minus h, x minus k. And a lot of times, this might be helpful to think of these as in parentheses on their own because you're doing x minus the value h, y minus the value k. \u003cbr/\u003e\u003cbr/\u003eSo why that's important is because if I was going to put these in parenthesis here, you can see that h is equal to 2. h is not negative 2. h is 2. So when I'm trying to find my vertex, I'm going to have 2. \u003cbr/\u003e\u003cbr/\u003eAnd then here, well, the easiest way to write this is y minus a negative 1 because y minus a negative 1, that's y minus k. Well, minus a negative 1 is the same thing as plus, so that's why it's always going to be kind of we think about it as the opposite. So my vertex though ends up being 2 comma negative 1. \u003cbr/\u003e\u003cbr/\u003eNow to identify the vertex, so I focus [INAUDIBLE] see my previous video. If you remember, I plotted them. And I think plotting them is so important to just visualize and understand where exactly everything means, how it's orientated, and just so you can actually find the points as well. So also if you have a problem where you actually have to graph this, just my rough sketch should be able to help you out as well. \u003cbr/\u003e\u003cbr/\u003eOK, so the first thing I'm going to do is since now I have that vertex information, I'm going to plot it. So that's at positive 2, negative 1, and I label it vertex so I don't forget. Now remember, the graph either opens up or down. That's why I wrote that up there so I don't forget it. \u003cbr/\u003e\u003cbr/\u003eThe next thing we need to do is figure out the value p. Remember p represents the distance from the vertex to the focus. If p is positive, then the graph either opens up, or opens up to the right. If p is negative, the graph either opens down or opens up the left depending on the orientation of the parabola. \u003cbr/\u003e\u003cbr/\u003eSo to find p, remember p is going to be your coefficient of your linear term. So my linear term here is why. My linear term over here is x. \u003cbr/\u003e\u003cbr/\u003eSo whatever that is 4p is equal to it. So in this case, you can see my value is 12, so I'm going to write for p is equal to 12. Solve for p. p is equal to 3. \u003cbr/\u003e\u003cbr/\u003eNow, again, my graph either opens up or down. So since the value of p is 3, from my vertex I'm going to go up 1, 2, 3. And I'm going to label that my focus. So now I know my graph opens up towards its focus, so it's going to open up to the right. \u003cbr/\u003e\u003cbr/\u003eBut remember, the opposite of p is going to be the distance from the vertex to the directrix. So that's going to be down 1, 2, 3. OK, so all we need to do for these problems is label the focus, so my focus is a coordinate point.\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv class='rp-report'\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='resource-details-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='resource-details-heading'\u003eResource Details\u003c/h2\u003e\n\u003cdiv class='rp-resource-details clearfix'\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eCurator Rating\u003c/dt\u003e\n\u003cdd\u003e\u003cspan class=\"star-rating\" aria-label=\"4.0 out of 5 stars\" role=\"img\"\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003ci class=\"fa-regular fa-star text-action\" aria-hidden=\"true\"\u003e\u003c/i\u003e\u003c/span\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt class=\"educator-rating-title\"\u003eEducator Rating\u003c/dt\u003e\u003cdd\u003e\u003cdiv class=\"educator-rating-details\" data-path=\"/educator_ratings/rrp_data?resourceable_id=154944\u0026amp;resourceable_type=Boclips%3A%3AVideoMetadata\"\u003e\u003cspan class=\"not-yet-rated\"\u003eNot yet Rated\u003c/span\u003e\u003c/div\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eMedia Length\u003c/dt\u003e\n\u003cdd\u003e14:15\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eGrade\u003c/dt\u003e\u003cdd title=\"Grade\"\u003e12th - Higher Ed\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eSubjects\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?keywords=business+ethics+case+study\u0026amp;search_tab_id=1\u0026amp;subject_ids%5B%5D=365220\"\u003eMath\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\u003cdd class=\"text-muted\"\u003e\u003ci class=\"fa-solid fa-lock mr5\"\u003e\u003c/i\u003e1 more...\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eMedia Type\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?keywords=business+ethics+case+study\u0026amp;search_tab_id=2\u0026amp;type_ids%5B%5D=4543647\"\u003eInstructional Videos\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eSource:\u003c/dt\u003e\n\u003cdiv class='preview-source' data-animation='true' data-boundary='.rp-info' data-container='.rp-resource-details' data-html='false' data-title='I teach math from the perspective of the struggling student because that was me \u0026amp; it could be you, too. 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