{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='MASTER Graphing a quadratic function in vertex form, identify vertex, axis of symmetry and domain' data-url='/boclips/videos/636738fbdc85e4451bc6ff0c' data-video-url='/boclips/videos/636738fbdc85e4451bc6ff0c' 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 Graphing a quadratic function in vertex form, identify vertex, axis of symmetry and domain\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'\u003eWelcome to McLogan. So what I'd like to do is show you how to graph a quadratic when it's in vertex form. Now, when graphing a quadratic in vertex form, it's very important to know two things, one, what exactly is vertex form. And I...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eWelcome to McLogan. So what I'd like to do is show you how to graph a quadratic when it's in vertex form. Now, when graphing a quadratic in vertex form, it's very important to know two things, one, what exactly is vertex form. And I guess I did not write vertex form anywhere, so let's go ahead and write vertex form right over here. \u003cbr/\u003e\u003cbr/\u003eSo vertex form is y equals a times x minus h squared plus k. Now, what's nice about vertex form is, we can easily identify the vertex as just h comma k. And also we can identify the axis of symmetry as x equals h. So it's really easy to be able to figure out what the vertex is as well as the axis symmetry and that's going to help us graph it. \u003cbr/\u003e\u003cbr/\u003eNow, for these six examples, I'm going to graph them when a is equal to 1, which should make it even nicer and easier. So the first thing I'm going to do is, I'm going to graph what the parent graph looks like. So the parent graph is just going to be if I was just going to graph f of x equals x squared. \u003cbr/\u003e\u003cbr/\u003eNow, it's very important for you to understand if you were to use a table of values, then the graph would go up over 1, up 1; over 1, up 1; over 2, up 4; over 2, up 4. Because if you plugged in some numbers, you can plug in. 1 squared is 1. If you plug in 2, 2 squared is 4. So when you go ahead and connect these, what you have is the shape of our quadratic, which we call a parabola or a lot of times people call it like the U-shaped graph. It looks like a U. \u003cbr/\u003e\u003cbr/\u003eSo basically what we're going to do is, we're going to identify what exactly is the new vertex and then just basically redraw that graph. Since our a is going to be 1 in all these cases, a negative 1 in a couple, but since the absolute value of a is equal to 1, there's not going to be any compression or stretching. So therefore, I'm basically just going to take this graph and move it around. \u003cbr/\u003e\u003cbr/\u003eNow, the easiest way to do that is to identify the vertex. So in this example, you can see that the vertex is at 0, 0. But now when we look at our new equation, you can see that h-- I don't have a value for h, so there's no x minus anything. So therefore, h is going to be 0, and k is going to be 2 because that's what I'm adding over to my function. \u003cbr/\u003e\u003cbr/\u003eSo my new vertex is going to be at 0 comma 2. And we're going to want to write that out. So for this example, my vertex-- again, I'm not adding or subtracting inside the function, so my vertex is going to be 0 for h and then 2 for k. The axis of symmetry is still going to be x equals h, so therefore, that's going to be x equals 0. \u003cbr/\u003e\u003cbr/\u003eSo all I'm simply do is just taking this graph and shifting it up 2 units. So I'm still going to go over 1, up 1; over 1, up 1; then over 2, up 4-- 1, 2, 3, 4. And then the axis of symmetry is right there on the y-axis. \u003cbr/\u003e\u003cbr/\u003eNow, in this example, you can see that I'm not adding or subtracting anything outside. See how I'm adding 2 outside the function? Here is subtracting 2 inside the function. But the other important thing to remember about this is it's x minus h. So therefore, it's x minus h, so it's x minus 2. Therefore, h is equal to 2, which is a very common mistake with students. \u003cbr/\u003e\u003cbr/\u003eSo therefore, I can write in the vertex is going to be 2 comma-- well, I could really just write plus 0 because I'm not adding anything-- 2 comma 0. So therefore, rather than shifting the graph negative 2, my h is actually positive 2 because it's h minus 2 or x minus h. x minus 2 to. 2 and h are equal. So therefore, it's plus 2, so therefore, I'm basically shifting this graph 2 units over. \u003cbr/\u003e\u003cbr/\u003eSo if I had a scale here-- 1, 2. So therefore, my new vertex is going to be at 2 comma 0. Now, all I simply need to do is follow, again, the same pattern of my parent graph. Go over 1, up 1; over 2, up 4-- 1, 2, 3, 4-- over 1, up 1, and you can always use the axis of symmetry here. The axis is x equals h, which in this case is 2. \u003cbr/\u003e\u003cbr/\u003eSo I can draw a nice little vertical line here, and by doing that vertical line, whatever points to the left, I can reflect over to the right. Then I just connect and make this nice little shaped U graph. \u003cbr/\u003e\u003cbr/\u003eOne thing that I did forget to do is talk about domain and range, and I figured that this would be a great opportunity to go and do that. So let's actually go back here real quick to this example. If we look at the black graph, the domain is going to be the set of all x values that make up that graph. Well, you can see, as this graph is going up, it's continuing to expand.\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=170891\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\u003e15:05\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?grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\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?grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\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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