{"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='Quadratic Inequalities' data-url='/boclips/videos/634c070ae5f7455d0b80639a' data-video-url='/boclips/videos/634c070ae5f7455d0b80639a' 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\nQuadratic Inequalities\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=\"30356647\" href=\"/search?publisher_ids%5B%5D=30356647\"\u003eFuseSchool\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'\u003eCREDITSAnimation \u0026amp; Design: Jean-Pierre Louw Narration: Lucy BillingsScript: Lucy BillingsYou probably already know that quadratic equations look like this... We can also have quadratic inequalities... We use inequalities to show us a...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eCREDITS\u003cbr/\u003eAnimation \u0026 Design: Jean-Pierre Louw \u003cbr/\u003eNarration: Lucy Billings\u003cbr/\u003eScript: Lucy Billings\u003cbr/\u003e\u003cbr/\u003eYou probably already know that quadratic equations look like this... We can also have quadratic inequalities... We use inequalities to show us a range of possible\u003cbr/\u003evalues… which actually has many real life uses.\u003cbr/\u003e\u003cbr/\u003eFor example, I might use them to work out that I need to film a racecar between 10 and 15 seconds after the start of the race. And they’re used throughout finance, such as working out what loan you can afford based on your\u003cbr/\u003eexpenditure.\u003cbr/\u003e\u003cbr/\u003eWe solve quadratic inequalities in pretty much the same way we solve quadratic equations, but also making use of the graph to help us work out which part we want… let’s have a look at an example. Solve it like you normally would… so factorise, quadratic formula or complete the square. This one factorises. \u003cbr/\u003e\u003cbr/\u003eNotice how i’ve changed it to be equals now. Solve each bracket, x equals 3 and x equals negative 2. Sketch what this quadratic looks like… U shaped, crossing the x-axis at -2 and 3. It’s just a rough sketch to help yourself in answering the question, so don’t worry too much about it at all. Because we want where the quadratic is LESS THAN zero. We want this part of the graph - the part that is less\u003cbr/\u003ethan 0 for y but also has the quadratic in.\u003cbr/\u003e\u003cbr/\u003eThis means the answer is x is greater than or equal to negative 2 but less than or equal to 3. Because we’ve shaded one joined region, the answer is one inequality. \u003cbr/\u003eIt’s this inequality sign because that was in the question.\u003cbr/\u003e\u003cbr/\u003eBecause we have 2 separate regions shaded, this means we have 2 separate inequality answers. Where x is less than negative 4 And where x is greater than negative 2. Because the question was a “greater than” inequality, that’s what our answers are…No “or equal to” involved. And that’s all there is to solving quadratic\u003cbr/\u003einequalities. You just need to do a little sketch of the graph, and work out the values from there.\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=\"4.5 out of 5 stars\" role=\"img\"\u003e\u003ci class=\"fa-solid fa-star text-action\" 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