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Kompas.com - 29/11/2022, 17:00 WIB
Silmi Nurul Utami
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Sifat grafik fungsi kuadrat berdasarkan nilai D(Kompas.com/SILMI NURUL UTAMI)
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KOMPAS.com – Fungsi kuadrat memiliki solusi atau akar persamaan yang digambarkan dalam nilai d. Nilai d disebut juga sebagai diskriminan, dan memiliki pengaruh pada fungsi kuadrat dan juga grafik fungsinya.
Untuk lebih memahaminya, berikut adalah pengaruh nilai D pada fungsi kuadrat!
Contoh soal 1
Tentukan fungsi-fungsi yang D>0. Apa kesamaan fungsi-fungsi ini?
Jawaban:
D>0 adalah diskriminan fungsi kuadrat yang lebih besar dari 0 atau bernilai positif. D>0 berarti grafik fungsi kuadratnya memotong sumbu x di dua titik.
Sehingga, fungsi kuadratnya memiliki dua akar nyata yang berbeda berupa bilangan real.
Baca juga: Sifat-sifat Grafik Fungsi Kuadrat
Artikel Kompas.id
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Contoh soal 2
Tentukan fungsi-fungsi yang D=0. Apa kesamaan fungsi-fungsi ini?
Jawaban:
D=0 adalah diskriminan fungsi kuadrat yang sama dengan atau bernilai 0. D=0 berarti grafik fungsi kuadratnya bersinggungan dengan sumbu x di satu titik.
Sehingga, fungsi kuadratnya memiliki dua akar nyata berupa bilangan real dengan nilai yang sama (akar kembar).
Contoh soal 3
Tentukan fungsi-fungsi yang D<0. Apa kesamaan fungsi-fungsi ini?
Jawaban:
D<0 adalah diskriminan fungsi kuadrat yang lebih kecil dari 0 atau bernilai negatif. D=0 berarti grafik fungsi kuadratnya tidak memotong maupun bersingungan dengan sumbu x.
Baca juga: Ciri-ciri Fungsi Kuadrat
Sehingga, fungsi kuadratnya tidak memiliki akar nyata dan hanya memiliki bilangan imajiner (akar imajiner) yang tidak nyata.
Contoh soal 4
Untuk setiap fungsi f(x) = ax² +bx + c, yang diberikan dalam a-j, hitunglah nilai D = b²-4ac.
- f(x) = -x²
- f(x) = x²– 2x – 3
- f(x) = -x²– x + 2
- f(x) = 3x²– 6x – 9
- f(x) = -2x²– 2x + 4
- f(x) = 2x²– 4x + 2
- f(x) = -x²+ 4x – 4
- f(x) = 2x²+ 4x + 2
- f(x) = -3x²– 12x – 15
- f(x) = 2x²+ 1
Jawaban:
Nilai D atau diskriminan fungsi kuadrat dirumuskan melalui D = b²– 4ac. Perlu diingat bahwa bentuk umum fungsi kuadrat adalah f(x) = ax²+ bx + c.
- f(x) = -x²
D = b²– 4ac = 0 - f(x) = x²– 2x – 3
D = b²– 4ac = (-2)² – 2.1.(-3) = 4 – (-12) = 16 - f(x) = -x²– x + 2
D = b²– 4ac = (-1)² – 4.(-1).2 = 1 – (-8) = 9 - f(x) = 3x² – 6x – 9
D = b² – 4ac = (-6)² – 4.3.(-9) = 36 – (-108) = 144 - f(x) = -2x² – 2x + 4
D = b² – 4ac = (-2)² – 4.(-2).4 = 4 – (-32) = 36 - f(x) = 2x² – 4x + 2
D = b² – 4ac = (-4)² – 4.2.2 = 16 – 16 = 0 - f(x) = -x² + 4x – 4
D = b² – 4ac = 4² – 4.(-1).(-4) = 16 – 16 = 0 - f(x) = 2x² + 4x + 2
D = b² – 4ac = 4² – 4.2.2 = 16 – 16 = 0 - f(x) = -3x² – 12x – 15
D = b² – 4ac = (-12)² – 4.(-3).(-15) = 144 – 180 = -36 - f(x) = 2x² + 1
D = b² – 4ac = - 4.2.1 = -8
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Tag
- diskriminan
- fungsi kuadrat
- materi matematika kelas 10
- grafik fungsi kuadrat
- nilai D pada fungsi kuadrat
- Soal dan Jawaban Karakteristik Fungsi Kuadrat
- Sifat-sifat Grafik Fungsi Kuadrat
- Ciri-ciri Fungsi Kuadrat
- Cara Menentukan Persamaan Grafik Fungsi Kuadrat
- Cara Menentukan Fungsi Kuadrat yang Melalui 3 Titik
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`); var wSpecStop = createElementFromHTML(`
Konten disembunyikan.
Muat ulang halaman untuk perbarui rekomendasi.
`); reactionPopup.querySelector('.buttonShare').setAttribute('data-title', item.title); reactionPopup.querySelector('.buttonShare').setAttribute('data-url', itemUrl); reactionPopup.querySelector('.buttonShare').setAttribute('data-campaign', 'AIML_Widget_Desktop'); let userFeedback = new UserFeedback(resultObj.engine['tracker_algsrc'], itemUrl + tracker_params, jxRecHelper, index); reactionPopup.querySelector('.buttonBookmark').addEventListener('click', function() { do_bookmark(itemUrl, index, userFeedback); }); reactionPopup.querySelector('.buttonShare').addEventListener('click', function() { userFeedback.event('share'); }); reactionPopup.querySelector('.buttonNotInterest').addEventListener('click', function() { if (getCookie('kmps_usrid')) { hideThisArt(this); userFeedback.event('not-interested'); } else { const parentAction = this.parentElement.parentElement.parentElement if (!!parentAction) { let indexElement = parentAction.getAttribute('data-index') if (indexElement != 'undefined') { localStorage.setItem('reaction_not_interest_temp', JSON.stringify({ urlpage: items[indexElement].url })) } } window.location.href = "https://account.kompas.com/login/a29tcGFz/" + btoa(window.location.href); } }); /** * trigger action "userFeedback" that user not interest item before, when not interest without login */ if (getCookie('kmps_usrid') && localStorage.getItem('reaction_not_interest_temp')) { const tempUrlNotInterest = JSON.parse(localStorage.getItem('reaction_not_interest_temp')) if (itemUrl == tempUrlNotInterest.urlpage) { userFeedback.event('not-interested'); localStorage.removeItem('reaction_not_interest_temp'); } } wSpecStop.querySelector('.wSpec-stop-undo').addEventListener('click', function() { showThisArt(this); userFeedback.event('un-not-interested'); }); recItem.appendChild(buttonOption); recItem.appendChild(reactionPopup); recItem.appendChild(wSpecStop); } var recItemWrapperA = createElement('a', null, null, null); recItemWrapperA.setAttribute('href', itemUrl + tracker_params); var titleDiv = createElement('h4', null, null, [cssClasses.title]); var titleTextNode = document.createTextNode(item.title); if (item.itemType == 'video') { var iconVideo = createElement('div', null, null, ['icoInline', 'icoVideo']); iconVideo.style.marginRight = '5px'; titleDiv.appendChild(iconVideo); } titleDiv.appendChild(titleTextNode); var sourceDiv = null; if (item.hasOwnProperty('method')) { sourceDiv = createElement('div', null, null, [cssClasses.source], resultObj.engine['type'] + ' . ' + item.method.toUpperCase()); } else { var sourceDiv = createElement('div', null, null, [cssClasses.source], resultObj.engine['type']); } var textWrapper = createElement('div', null, null, [cssClasses.text_wrapper]); textWrapper.appendChild(categoryDiv); textWrapper.appendChild(titleDiv); textWrapper.appendChild(sourceDiv); recItemWrapper.appendChild(imgWrapper); recItemWrapper.appendChild(textWrapper); recItemWrapperA.appendChild(recItemWrapper); recItem.appendChild(recItemWrapperA); widgetWrapper.appendChild(recItem); // hook up the click handler for this item // recItem.onclick = handleClick.bind(null, jxRecHelper, itemUrl + tracker_params, index); recItemWrapperA.onclick = handleClick.bind(null, jxRecHelper, itemUrl + tracker_params, index); }); } // end while var endDate = new Date(); var loadtime = (endDate.getTime() - startDate.getTime()); trackEventGa('AIML Article Recommendation', 'Content Loaded', 'algsrc='+algsrc+',site=SKOLA,device=desktop,loadtime=' + loadtime) let domain = window.location.hostname; if(domain=='www.kompas.com'){ var url=window.location.href.split("/"); domain=url[2]+'/'+url[3] } let user_subs_type = "Gues"; let subs_type = ""; let is_lgn = 0; let engine = algsrc; if(getCookie('kmps_usrid')){is_lgn=1}; let time_load = loadtime; resolve(); /*** * JXRECSDK NOTES 3 of 5 - * pass all the info about the items to the rec helper * each one is an object: ALL MANDATORY * div * id * pos */ jxRecHelper.items(widgetItemArr); /*** * JXRECSDK NOTES 4 of 5 - * Call the ready() of the helper object when the recommendation * results have been populated to the widget * (This will register the action=ready event) */ if (resultObj.engine['type'] == 'api-1') { jxRecHelper.ready(resultObj.options.algo + ":" + resultObj.options.version); } else { jxRecHelper.ready(resultObj.engine['type']); } } else { jxRecHelper.error(204); console.error("Error: no recommendation items"); return; } } catch (err) { jxRecHelper.error(901); console.log(err.stack); let domain = window.location.hostname; if(domain=='www.kompas.com'){ var url=window.location.href.split("/"); domain=url[2]+'/'+url[3] } let user_subs_type = "Gues"; let subs_type = "" let is_lgn = 0; let engine = algsrc; if(getCookie('kmps_usrid')){is_lgn=1}; let endDate = new Date(); let time_load = (endDate.getTime() - startDate.getTime()); } }); } const _jxRecSdkURL = 'https://scripts.jixie.media/jxrecsdk.1.0.min.js'; var startDate = new Date(); class OneWidget { constructor() { //this is also the one we will pass to the JX rec helper object when //we instantiate it: //In this implementation most of these come from the options obj //on the publisher page. this._options = { accountid: '9262bf2590d558736cac4fff7978fcb1', pageurl: 'https://www.kompas.com/skola/read/2022/11/29/170000269/soal-dan-jawaban-pengaruh-nilai-d-pada-fungsi-kuadrat', widget_id: '1000183-6xWeiWZFIM', type: 'pages', container: 'rekomendasi-konten-pilihan-untukmu-aiml', keywords: content_tags, title: title, customid: "69", count: 14, }; this._containerId = this._options.container; this._container = document.getElementById(this._containerId); this._engines = [{"url":"https:\/\/recommendation.jixie.media\/v1\/recommendation","method":"GET","pageurl":"https:\/\/www.kompas.com\/skola\/read\/2022\/11\/29\/170000269\/soal-dan-jawaban-pengaruh-nilai-d-pada-fungsi-kuadrat","system":"jx","type":"api-1","tracker_params":"?source=widgetML","tracker_algsrc":"V","count":14,"page_status":"read","excludeitemids":"20221129170000269"}]; } kickOff() { startDate = new Date(); const rand = Math.floor(Math.random() * 1000); /*const randSystem = Math.floor(Math.random() * 3); this._engine = this._engines[randSystem] if (location.hostname.indexOf('lestari') != -1) { this._engine = this._engines[1] }*/ this._engine = this._engines[0]; this._options.system = this._engine['system'] trackEventGa('AIML Article Recommendation', 'Widget load', 'algsrc=' + this._engine['tracker_algsrc'] + ',site=SKOLA,device=desktop') let promJXSDK = fetchJSFileP(_jxRecSdkURL); let thisObj = this; // first we wait on the JX REC SDK to be loaded and initialized let recHelperObj = null; let recResults = null; promJXSDK .then(function() { /*** * JXRECSDK NOTES 1 of 5 - INSTANTIATION OF A JX REC HELPER OBJECT * Call this AFTER JX REC SDK is loaded but BEFORE you call your REC * backend. * * param: MANDATORY options object * options object must at a minimal have * accountid: get from jixie * widgetid: get from jixie * container: DIV ID of the destination div to house the widget * (for jixie widget this is just the options object passed from the page) * * (This will also register the action=load event) */ recHelperObj = jxRecMgr.createJxRecHelper(thisObj._options); let basicInfo = thisObj._options; basicInfo.engine = thisObj._engine if (basicInfo.engine.type == 'api-1') { var options = { count: basicInfo['count'], adpositions: "", keywords: basicInfo['keywords'], title: basicInfo['title'], date_published: "2022-11-29", pagecategory: "SKOLA", algo: "mixed" }; if(getCookie('kmps_usrid')){ var kg = { pagetype:basicInfo.engine.page_status, uid:getCookie('kmps_usrid'), ukid:getCookie('kmp_uid') } if(basicInfo.engine.page_status=='read'){ kg['excludeitemids'] = basicInfo.engine.excludeitemids; kg['multiFormat'] = true; } options['additional'] = { kg:kg }; } return recHelperObj.getJxRecommendations(options); } else { return fetchRecommendationsP(basicInfo, recHelperObj.getJxUserInfo()); } }) .then(function(resp) { if (thisObj._engine.type == 'api-3') { recResults = new Object recResults.items = resp.docs.result; } else { recResults = resp; } recResults.engine = thisObj._engine; if (!resp || !recResults.items || recResults.items.length == 0) { /*** * JXRECSDK NOTES 2 of 5 - * Call the error() function on the recHelper when either an error * has occured in the fetching or there are no recommended items * * (This will register the action=error event) */ recHelperObj.error(204); throw "no recommendation results"; } }) .then(function() { // everything is ready (recommendation results, css): document.getElementById("rekomendasi-konten-pilihan-untukmu-aiml").classList.remove("-loading"); document.querySelector('.wSpec-list').remove(); createDisplay(rand, thisObj._container, recResults, recHelperObj) .then(function() { toggleDropdown(); //observe lozad lozad('.lozad', { load: function(el) { el.src = el.dataset.src; el.onload = function() { el.classList.add('fade') } } }).observe() }) }) .catch(function(error) { console.log(`Unable to create recommendations widget ${error.stack} ${error.message}`); }); } } var limit_gtm_ready = 1; function check_gtm_ready() { if ('ga' in window) { // create a new instance of our widget based on the options const newW = new OneWidget(); newW.kickOff(); } else { const timeout_gtm_ready = setTimeout(check_gtm_ready, 500) limit_gtm_ready += 1; if (limit_gtm_ready > 10) { clearTimeout(timeout_gtm_ready); const newW = new OneWidget(); newW.kickOff(); } } } check_gtm_ready() document.querySelector('.wSpec-secret').addEventListener('click', function(e) { e.preventDefault(); let wSl = document.querySelectorAll('.wSpec-source'); if (wSl.length > 0) { for (let i = 0; i < wSl.length; i++) { wSl[i].classList.toggle('show') } } }) function trackEventGa(category, action, label) { if ("ga" in window) { ga(function() { tracker = ga.getAll()[0]; if (tracker) { tracker.send("event", category, action, label); console.log('track event ', category, action, label) } }) } } function formBody(obj) { let formBody = []; for (var property in obj) { let encodedKey = encodeURIComponent(property); let encodedValue = encodeURIComponent(obj[property]); formBody.push(encodedKey + "=" + encodedValue); } return formBody.join("&"); } function getCookie(name) { var name = name + '='; var cookies = decodeURIComponent(document.cookie).split(';'); for (var i = 0; i < cookies.length; i++) { var c = cookies[i]; while (c.charAt(0) == ' ') { c = c.substring(1); } if (c.indexOf(name) == 0) { return c.substring(name.length, c.length); } } } function get_guid(url) { const videoPath = url.match(/\/watch\/(\d+)/); if (videoPath) { return `video.${videoPath[1]}`; } let arrayUrl = url.split('/'); let readPath = arrayUrl.indexOf('read'); if (arrayUrl[readPath + 1] == 'xml') { readPath += 1; } let year = arrayUrl[readPath + 1]; let month = arrayUrl[readPath + 2]; let date = arrayUrl[readPath + 3]; let id = arrayUrl[readPath + 4]; let guid = `.xml.${year}.${month}.${date}.${id}`; return guid; } function toggleDropdown() { let tdd = document.querySelectorAll('[data-dropdown]') if (!!tdd) { tdd.forEach((el) => { el.addEventListener('click', function() { el.parentElement.classList.toggle('-active') let saved = el.parentElement.getAttribute('data-saved') let kmps_usrid = getCookie('kmps_usrid'); if (kmps_usrid && !saved && el.parentElement.classList.contains('-active')) { let url = el.parentElement.getAttribute('data-url'); let guid = get_guid(url); check_bookmark( kmps_usrid, guid ).then(function(resp) { if (resp.hasOwnProperty('total_data')) { if (resp.total_data > 0) { el.parentElement.querySelector('.buttonBookmark').classList.add('-active'); el.parentElement.querySelector('.buttonBookmark').innerHTML = 'Hapus dari tersimpan'; el.parentElement.setAttribute('data-saved', 'true'); } else { el.parentElement.setAttribute('data-saved', 'false'); } } }) } }) document.addEventListener("click", function(e) { // console.log(e.target) if (el.contains(e.target)) { // console.log(tdd) } else { el.parentElement.classList.remove('-active') } }); }); } } function check_bookmark(kmps_usrid, guid) { let url = `https://api.kompas.com/2021/reaction/bookmark/list?kmps_usrid=${kmps_usrid}&guid=${guid}`; return new Promise(function(resolve, reject) { var xmlhttp = new XMLHttpRequest(); xmlhttp.onreadystatechange = function() { if (this.readyState == 4 && this.status == 200) { resolve(JSON.parse(this.responseText)) } }; xmlhttp.open("GET", url, true); xmlhttp.send(); }); } function do_bookmark(pageurl, pos, userFeedback) { const wSpecItem = document.querySelector(`.wSpec-item[data-index="${pos}"]`); const btnBookmark = wSpecItem.querySelector('.buttonBookmark'); const kmps_usrid = getCookie('kmps_usrid'); const guid = get_guid(pageurl); const type = pageurl.match(/\/watch\/(\d+)/) ? 'video' : 'article'; if (kmps_usrid) { if (btnBookmark.classList.contains('-active')) { set_unbookmark({ guid: guid, kmps_usrid: kmps_usrid, type: type }).then(function(resp) { btnBookmark.classList.remove('-active'); btnBookmark.innerHTML = 'Simpan artikel'; reactionToast('Artikel berhasil dihapus dari list yang disimpan'); userFeedback.event('un-save'); }).catch(function(resp) { // message: "Data doesn't exists" if (resp.hasOwnProperty('message') && resp.message.includes('exist')) { btnBookmark.classList.remove('-active'); btnBookmark.innerHTML = 'Simpan artikel'; reactionToast('Artikel berhasil dihapus dari list yang disimpan'); } }) } else { const user_bookmark_url = "https://activity.kompas.com/saved?order=desc"; set_bookmark({ guid: guid, kmps_usrid: kmps_usrid, type: type, publisher: 'kompas', platform: 'desktop' }).then(function(resp) { btnBookmark.classList.add('-active'); btnBookmark.innerHTML = 'Hapus dari tersimpan'; reactionToast('Artikel berhasil disimpan', user_bookmark_url); userFeedback.event('save'); }).catch(function(resp) { // message: "Data already exist" if (resp.hasOwnProperty('message') && resp.message.includes('exist')) { btnBookmark.classList.add('-active'); btnBookmark.innerHTML = 'Hapus dari tersimpan'; reactionToast('Artikel berhasil disimpan', user_bookmark_url); } }) } } else { const login_url = "https://account.kompas.com/login/a29tcGFz/" + btoa(window.location.href); window.location.href = login_url; } } function set_bookmark(data) { const url = "https://api.kompas.com/2021/reaction/bookmark/add"; return new Promise(function(resolve, reject) { const xmlhttp = new XMLHttpRequest(); xmlhttp.onreadystatechange = function() { if (this.readyState == 4 && this.status == 201) { resolve(JSON.parse(this.responseText)); } else if (this.readyState == 4 && this.status == 400) { reject(JSON.parse(this.responseText)); } }; xmlhttp.open("POST", url, true); xmlhttp.setRequestHeader("Content-Type", "application/x-www-form-urlencoded;charset=UTF-8"); xmlhttp.send(formBody(data)); }); } function set_unbookmark(data) { const url = "https://api.kompas.com/2021/reaction/bookmark/delete"; return new Promise(function(resolve, reject) { const xmlhttp = new XMLHttpRequest(); xmlhttp.onreadystatechange = function() { if (this.readyState == 4 && this.status == 200) { resolve(JSON.parse(this.responseText)); } else if (this.readyState == 4 && this.status == 400) { reject(JSON.parse(this.responseText)); } }; xmlhttp.open("POST", url, true); xmlhttp.setRequestHeader("Content-Type", "application/x-www-form-urlencoded;charset=UTF-8"); xmlhttp.send(formBody(data)); }); } class UserFeedback { constructor(engine, pageurl, jxRecHelper, pos) { this.engine = engine; this.pageurl = pageurl; this.jxRecHelper = jxRecHelper; this.pos = pos; } event(feedback) { if (this.engine == 'C') { const xmlhttp = new XMLHttpRequest(); let params = { domain: 'kompas.com', ce_userid: getCookie('kmps_usrid'), ce_sessionid: getCookie('ukid'), ce_pageurl: this.pageurl, engine: 'C', ce_feedback: feedback } xmlhttp.open("GET", 'https://apis.kgdata.dev/v1/aiml/feedback-widgetml' + formatParams(params)); xmlhttp.send(); } else if (this.engine == 'V') { if (feedback == 'share') { this.jxRecHelper.shared(this.pos); } else if (feedback == 'save') { this.jxRecHelper.bookmarked(this.pos); } else if (feedback == 'not-interested') { this.jxRecHelper.hidden(this.pos); } else if (feedback == 'un-not-interested') { this.jxRecHelper.unhidden(this.pos); } } } } function formatParams(params) { return "?" + Object .keys(params) .map(function(key) { return key + "=" + encodeURIComponent(params[key]) }) .join("&") } document.addEventListener("click", function(e){ let dx = document.querySelectorAll('[data-dropdown]') if(dx) { dx.forEach(function(el){ if(el.contains(e.target)) { el.parentElement.classList.toggle('-active') } else { el.parentElement.classList.remove('-active') } }) } })
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