{"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-af73c33d.css\" media=\"all\" /\u003e\n\u003cdiv data-title='MASTER How to graph a quadratic in standard form using the formula for axis of symmetry and vertex' data-url='/boclips/videos/636738fbe1a05d2baafac370' data-video-url='/boclips/videos/636738fbe1a05d2baafac370' 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 How to graph a quadratic in standard form using the formula for axis of symmetry and vertex\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, ladies and gentlemen. So what I'd like to do is show you how to graph a quadratic using the equation for a vertex as well as axis of symmetry. Now, I have two functions and I have two equations, and they're basically going to be...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eWelcome, ladies and gentlemen. So what I'd like to do is show you how to graph a quadratic using the equation for a vertex as well as axis of symmetry. \u003cbr/\u003e\u003cbr/\u003eNow, I have two functions and I have two equations, and they're basically going to be the exact same thing. It's just a little bit different. But I'm not really sure what type of study you're doing as far as quadratic functions or quadratic equations, so the way my explanation is going to work, I'm going to change it kind of for both of those. \u003cbr/\u003e\u003cbr/\u003eHowever, the standard form kind of applies. When you have a quadratic in standard form, you can either complete the square, rewrite it in vertex form, and graph using our transformations, or we can identify the axis of symmetry as well as the vertex. \u003cbr/\u003e\u003cbr/\u003eSo the main important thing here is identifying the axis of symmetry. So the axis of symmetry is so important because that's going to be the line that the graph is symmetrical about. So it also helps us because we can graph one side of the quadratic over a parabola and then flip it to graph the other side. \u003cbr/\u003e\u003cbr/\u003eSo the axis of symmetry is x equals opposite of b divided by 2 times a. Remember that's for all quadratics in the form ax squared plus bx plus c. \u003cbr/\u003e\u003cbr/\u003eSo, therefore, in this case, I basically have negative 6 divided by 2 times 1 equals negative 6 divided by 2, which equals negative 3. Therefore, my axis of symmetry is a line, x equals negative 3. \u003cbr/\u003e\u003cbr/\u003eSo when graphing this, that's the first thing we're going to want to do. And that's going to basically give me an understanding of where this axis of symmetry-- where this graph is symmetrical about. \u003cbr/\u003e\u003cbr/\u003eSo I draw out a nice little dashed line because x equals 3 creates a vertical line. So, therefore, I know that this line not only cuts my parabola in half, but also that is going to be where my vertex-- the main important point on a parabola-- that's where my vertex is going to lie. \u003cbr/\u003e\u003cbr/\u003eSo by using that understanding, if I know that the axis of symmetry has an x value of negative 3, well, guess what? The vertex, since it lies on the axis of symmetry, the x value of the vertex-- because the vertex is a point where the axis of symmetry's line is going to be opposite of b divided by 2 times a and then f of opposite of b divided by 2 times a.\u003cbr/\u003e\u003cbr/\u003eAnd this is what I was talking about, the difference between equations and functions. When we talk about functions, we talk about evaluating, right? If I had f of x equals 3x plus 1 and I say f of negative 1, then you plug in negative 1 in for x. All right. \u003cbr/\u003e\u003cbr/\u003eSo in this case, you're taking the x value. Then you're going to plug that x value in back to your function to find the output value, because basically in this case we have an x-axis and an f of x-axis, which is basically the same output as a y-axis if we were doing an equation. Basically represents the same thing, but the notation's a little bit differently. \u003cbr/\u003e\u003cbr/\u003eSo, anyways, I first need to figure out what my x value is, which is negative 3. Then to evaluate the vertex, my other point, I'm just going to do f of negative 3 because that's the x value of my vertex. \u003cbr/\u003e\u003cbr/\u003eSo I'm plugging that into my equation. I have negative 3 squared plus 6 times negative 3 plus 9. \u003cbr/\u003e\u003cbr/\u003eWell, negative 3 squared is going to be positive 9. 6 times negative 3 is negative 18 plus 9. Well, that's going to give me 0. \u003cbr/\u003e\u003cbr/\u003eTherefore, my vertex is at the coordinate point 0, 0. I'm sorry. It's at the coordinate point negative 3, 0. The vertex, OK? \u003cbr/\u003e\u003cbr/\u003eNow also to graph it, it's kind of helpful to, one, identify if the graph is going to be opening up or down. You can see my a is positive so I know my graph is going to be opening up. That's a good way to always check your work, make sure you're doing it correctly. \u003cbr/\u003e\u003cbr/\u003eNow, to find the remaining points, there's a couple ways you can do this. I see that this is-- my a is equal to 1. So, if you remember, when we were graphing the paragraph, when a is equal to 1, basically the relationship between the rest of the point or at least a couple points in the vertex was over 1, up 1, over 2, up 4. \u003cbr/\u003e\u003cbr/\u003eAnd that worked for a couple points, but that only works when a equals 1. Where you can see the rest of the problems here, I don't have that flexibility to be able to do that. \u003cbr/\u003e\u003cbr/\u003eSo one way to just kind of double check if you don't remember that is always kind of pick two points right next to your axis of symmetry. So I'll do negative 2 and negative 1. So I'll do f of negative 2 and I'll do f of negative 1.\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=162603\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\u003e19:39\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. My videos are short, to-the-point and cover everything from Algebra 1 through Calculus. I have a ton of content to share with you \u0026amp; hope you find them useful in whatever class you are taking!' data-trigger='hover focus'\u003e\n\u003cspan\u003eBrian McLogan\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-circle-info channel-tooltip-icon' id='channel-tooltip'\u003e\u003c/i\u003e\n\u003c/div\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eDate\u003c/dt\u003e\n\u003cdd\u003e2015\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-language'\u003e\u003c/i\u003e\n\u003cdt\u003eLanguage\u003c/dt\u003e\u003cdd\u003eEnglish\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eAudiences\u003c/dt\u003e\u003cdd\u003e\u003cspan\u003e\u003ca href=\"/search?audience_ids%5B%5D=371079\u0026amp;grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\u0026amp;search_tab_id=1\"\u003eFor Teacher Use\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\u003cdd class=\"text-muted\"\u003e\u003ci class=\"fa-solid fa-lock mr5\"\u003e\u003c/i\u003e2 more...\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eUsage Permissions\u003c/dt\u003e\u003cdd\u003eFine Print: Educational Use\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-materials-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-materials-heading'\u003eAdditional Materials\u003c/h2\u003e\n\u003cdiv class='additional-material'\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-lock'\u003e\u003c/i\u003e\n\u003ca class=\"text-muted\" title=\"Video Transcript\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\"\u003eVideo Transcript\u003c/a\u003e\n\u003c/div\u003e\n\u003cdiv class='additional-material'\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-lock'\u003e\u003c/i\u003e\n\u003ca class=\"text-muted\" title=\"Video Preview\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\"\u003eVideo Preview\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='concepts-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='concepts-heading'\u003eConcepts\u003c/h2\u003e\n\u003cdiv class='clearfix'\u003e\n\u003cdiv class='details-list concepts' data-identifier='Boclips::VideoDecorator636738fbe1a05d2baafac370' data-type='concepts'\u003evertex, standard form, graphing, real numbers, symmetry, opposite, infinity, values, domain, axis of symmetry, line of symmetry\u003c/div\u003e\n\u003cdiv class='concepts-toggle-buttons' data-identifier='Boclips::VideoDecorator636738fbe1a05d2baafac370'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-tags-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-tags-heading'\u003eAdditional Tags\u003c/h2\u003e\n\u003cdiv class='clearfix'\u003e\n\u003cdiv class='details-list keyterms' data-identifier='Boclips::VideoDecorator636738fbe1a05d2baafac370' data-type='keyterms'\u003emaths, how to, help me with math, how to graph a quadratic, how to graph a parabola, parabola, quadratic, equation of axis of symmetry ib math studies, ib math studies how to plot an axis of symmetry, graph, function, math help, algebra, graphing quadratic equations, quadratics, graphing parabolas, how to find the axis of symmetry, how to find the vertex, आलेख कैसे ग्राफ़ करें, how to graph quadratic in standard form, axis symmetry, couple points, equals opposite, negative infinity, axis, line, pick, multiplying, table, fraction, problem, bracket, points, point, choose, highest, represents, make, times, 2 times\u003c/div\u003e\n\u003cdiv class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator636738fbe1a05d2baafac370'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='classroom-considerations-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='classroom-considerations-heading'\u003eClassroom Considerations\u003c/h2\u003e\n\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eBest For: Explaining a topic\u003c/div\u003e\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eVideo is ad-free\u003c/div\u003e \n\u003c/div\u003e\n\u003cdiv aria-labelledby='educator-ratings-heading' class='rp-info-section'\u003e\n\u003ch2 class='title sr-only' id='educator-ratings-heading'\u003eEducator Ratings\u003c/h2\u003e\n\u003cdiv id=\"educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"all-educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"educator-rating-form-root\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-resource'\u003e\n\u003cdiv aria-label='Show resource details' class='rp-show-info' role='button' tabindex='0'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\nShow resource details\n\u003c/div\u003e\n\u003cdiv aria-label='Video player' class='player' id='player-wrapper' role='region'\u003e\n\u003cdiv class='relative container mx-auto' id='lp-boclips-visitor-thumbnail'\u003e\n\u003ca class=\"block\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" aria-label=\"Play video: MASTER How to graph a quadratic in standard form using the formula for axis of symmetry and vertex\" href=\"/subscription/new\"\u003e\u003cimg class=\"resource-img img-thumbnail img-responsive z-10 lp-boclips-thumbnail w-full h-full lozad\" alt=\"MASTER How to graph a quadratic in standard form using the formula for axis of symmetry and vertex\" title=\"MASTER How to graph a quadratic in standard form using the formula for axis of symmetry and vertex\" onError=\"handleImageNotLoadedError(this)\" data-default-image=\"https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/missing.png\" data-src=\"https://cdnapisec.kaltura.com/p/1776261/thumbnail/entry_id/1_di5qz9i8/width/250\" width=\"315\" height=\"220\" src=\"data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs\" /\u003e\n\u003cspan aria-hidden='true' class='flex justify-center items-center bg-white rounded-full w-16 h-16 absolute top-1/2 left-1/2 -mt-8 -ml-8 cursor-pointer z-0 border-2 border-primary drop-shadow-md lp-boclips-thumbnail-playBtn'\u003e\n\u003ci class='fa-solid fa-play text-primary text-3xl ml-1 drop-shadow-xl'\u003e\u003c/i\u003e\n\u003c/span\u003e\n\u003c/a\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n"}