<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    .main-wrap {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    /* SVG Graph styling */
    .graph-container {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      overflow: hidden;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    .grid-line {
      stroke: #f1f5f9;
      stroke-width: 1;
    }
    .axis {
      stroke: #94a3b8;
      stroke-width: 1.5;
    }
    .axis-tick-text {
      font-size: 11px;
      fill: #64748b;
      font-family: monospace;
      text-anchor: middle;
      dominant-baseline: middle;
      user-select: none;
    }

    .curve-parabola {
      fill: none;
      stroke: #8b5cf6;
      stroke-width: 3;
      stroke-linecap: round;
    }

    .curve-line {
      fill: none;
      stroke: #0d9488;
      stroke-width: 3;
      stroke-linecap: round;
    }

    .pt-marker {
      cursor: pointer;
      transition: r 0.2s ease, filter 0.2s ease;
    }
    .pt-marker:hover {
      filter: drop-shadow(0 0 4px rgba(0,0,0,0.25));
    }

    /* Equation Legend */
    .legend-row {
      display: flex;
      justify-content: center;
      gap: 16px;
      font-size: 13px;
      font-weight: 600;
    }
    .legend-item {
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .legend-swatch {
      width: 12px;
      height: 4px;
      border-radius: 2px;
    }
    .swatch-parabola { background: #8b5cf6; }
    .swatch-line { background: #0d9488; }

    /* Interactive tabs */
    .controls {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
    }

    .btn-toggle {
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #475569;
      padding: 8px 12px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: background 0.15s ease, border-color 0.15s ease, color 0.15s ease;
    }
    .btn-toggle.active {
      background: #eff6ff;
      border-color: #3b82f6;
      color: #1d4ed8;
      box-shadow: 0 0 0 1px #3b82f6;
    }

    /* Verification card */
    .verify-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      font-size: 13px;
    }

    .verify-row {
      display: flex;
      flex-direction: column;
      gap: 4px;
      padding: 6px 10px;
      background: #ffffff;
      border-radius: 6px;
      border: 1px solid #e2e8f0;
      transition: border-color 0.2s ease, background 0.2s ease;
    }
    .verify-row.highlight {
      border-color: #3b82f6;
      background: #f0f9ff;
    }

    .verify-title {
      display: flex;
      justify-content: space-between;
      align-items: center;
      font-weight: 700;
      color: #0f172a;
    }

    .badge-check {
      color: #16a34a;
      font-weight: 700;
      display: inline-flex;
      align-items: center;
      gap: 3px;
    }

    .calc-line {
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      font-size: 12px;
      color: #334155;
      display: flex;
      flex-wrap: wrap;
      gap: 8px;
    }
  </style>
</head>
<body>
  <div class="main-wrap">
    
    <div class="legend-row">
      <div class="legend-item">
        <span class="legend-swatch swatch-parabola"></span>
        <span>y = x² − 2</span>
      </div>
      <div class="legend-item">
        <span class="legend-swatch swatch-line"></span>
        <span>y = x</span>
      </div>
    </div>

    
    <div class="graph-container">
      <svg id="graphSvg" viewBox="0 0 350 350">
        
      </svg>
    </div>

    
    <div class="controls">
      <button id="btnA" class="btn-toggle active" onclick="selectPoint('A')">
        Point A (−1, −1)
      </button>
      <button id="btnB" class="btn-toggle" onclick="selectPoint('B')">
        Point B (2, 2)
      </button>
    </div>

    
    <div class="verify-card">
      <div id="cardA" class="verify-row highlight">
        <div class="verify-title">
          <span>Point A (−1, −1)</span>
          <span class="badge-check">✓ Both True</span>
        </div>
        <div class="calc-line">
          <span>Parabola: −1 = (−1)² − 2</span>
          <span>Line: −1 = −1</span>
        </div>
      </div>

      <div id="cardB" class="verify-row">
        <div class="verify-title">
          <span>Point B (2, 2)</span>
          <span class="badge-check">✓ Both True</span>
        </div>
        <div class="calc-line">
          <span>Parabola: 2 = (2)² − 2</span>
          <span>Line: 2 = 2</span>
        </div>
      </div>
    </div>
  </div>

  <script>
    // Coordinate mapping parameters
    // x: [-3, 4], y: [-3, 5]
    const xMin = -3, xMax = 4;
    const yMin = -3, yMax = 5;
    const padL = 30, padR = 20, padT = 20, padB = 25;
    const width = 350, height = 350;

    const plotW = width - padL - padR;
    const plotH = height - padT - padB;

    function mapX(x) {
      return padL + ((x - xMin) / (xMax - xMin)) * plotW;
    }
    function mapY(y) {
      return padT + ((yMax - y) / (yMax - yMin)) * plotH;
    }

    const svg = document.getElementById('graphSvg');

    // Build SVG Grid & Axes
    let content = '';

    // Grid lines & labels
    for (let x = xMin; x <= xMax; x++) {
      const px = mapX(x);
      content += `<line class="grid-line" x1="${px}" y1="${padT}" x2="${px}" y2="${height - padB}"/>`;
      if (x !== 0) {
        content += `<text class="axis-tick-text" x="${px}" y="${mapY(0) + 14}">${x}</text>`;
      }
    }

    for (let y = yMin; y <= yMax; y++) {
      const py = mapY(y);
      content += `<line class="grid-line" x1="${padL}" y1="${py}" x2="${width - padR}" y2="${py}"/>`;
      if (y !== 0) {
        content += `<text class="axis-tick-text" x="${mapX(0) - 12}" y="${py}">${y}</text>`;
      }
    }

    // Origin 0
    content += `<text class="axis-tick-text" x="${mapX(0) - 10}" y="${mapY(0) + 12}">0</text>`;

    // Main Axes
    const ox = mapX(0);
    const oy = mapY(0);
    content += `<line class="axis" x1="${padL}" y1="${oy}" x2="${width - padR}" y2="${oy}"/>`;
    content += `<line class="axis" x1="${ox}" y1="${padT}" x2="${ox}" y2="${height - padB}"/>`;

    // Axis Arrows / Labels
    content += `<text class="axis-tick-text" style="font-weight:700; fill:#475569;" x="${width - padR + 10}" y="${oy}">x</text>`;
    content += `<text class="axis-tick-text" style="font-weight:700; fill:#475569;" x="${ox}" y="${padT - 8}">y</text>`;

    // Sample Parabola y = x^2 - 2
    let dPara = '';
    const step = 0.05;
    for (let x = -2.6; x <= 2.6; x += step) {
      const y = x * x - 2;
      const px = mapX(x);
      const py = mapY(y);
      dPara += (dPara === '' ? `M ${px} ${py}` : ` L ${px} ${py}`);
    }
    content += `<path class="curve-parabola" d="${dPara}"/>`;

    // Sample Line y = x
    const xL1 = -3, yL1 = -3;
    const xL2 = 4, yL2 = 4;
    content += `<line class="curve-line" x1="${mapX(xL1)}" y1="${mapY(yL1)}" x2="${mapX(xL2)}" y2="${mapY(yL2)}"/>`;

    // Points A and B
    const ptAx = mapX(-1), ptAy = mapY(-1);
    const ptBx = mapX(2), ptBy = mapY(2);

    // Dynamic Elements group (markers & highlights)
    content += `
      <g id="pointAGroup" onclick="selectPoint('A')" style="cursor:pointer;">
        <circle id="haloA" cx="${ptAx}" cy="${ptAy}" r="12" fill="#3b82f6" opacity="0.25"/>
        <circle cx="${ptAx}" cy="${ptAy}" r="6" fill="#1e2945" stroke="#ffffff" stroke-width="2"/>
        <rect x="${ptAx - 52}" y="${ptAy - 26}" width="58" height="20" rx="4" fill="#1e2945"/>
        <text x="${ptAx - 23}" y="${ptAy - 13}" fill="#ffffff" font-size="11" font-weight="bold" font-family="sans-serif" text-anchor="middle" dominant-baseline="middle">A (−1, −1)</text>
      </g>

      <g id="pointBGroup" onclick="selectPoint('B')" style="cursor:pointer;">
        <circle id="haloB" cx="${ptBx}" cy="${ptBy}" r="12" fill="#3b82f6" opacity="0"/>
        <circle cx="${ptBx}" cy="${ptBy}" r="6" fill="#1e2945" stroke="#ffffff" stroke-width="2"/>
        <rect x="${ptBx + 8}" y="${ptBy - 24}" width="54" height="20" rx="4" fill="#1e2945"/>
        <text x="${ptBx + 35}" y="${ptBy - 11}" fill="#ffffff" font-size="11" font-weight="bold" font-family="sans-serif" text-anchor="middle" dominant-baseline="middle">B (2, 2)</text>
      </g>
    `;

    svg.innerHTML = content;

    function selectPoint(pt) {
      const btnA = document.getElementById('btnA');
      const btnB = document.getElementById('btnB');
      const cardA = document.getElementById('cardA');
      const cardB = document.getElementById('cardB');
      const haloA = document.getElementById('haloA');
      const haloB = document.getElementById('haloB');

      if (pt === 'A') {
        btnA.classList.add('active');
        btnB.classList.remove('active');
        cardA.classList.add('highlight');
        cardB.classList.remove('highlight');
        haloA.setAttribute('opacity', '0.25');
        haloB.setAttribute('opacity', '0');
      } else {
        btnB.classList.add('active');
        btnA.classList.remove('active');
        cardB.classList.add('highlight');
        cardA.classList.remove('highlight');
        haloB.setAttribute('opacity', '0.25');
        haloA.setAttribute('opacity', '0');
      }
    }
  </script>
</body>
</html>

Understanding Linear-Quadratic Systems

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      background: #f8f9fa;
      color: #1e2945;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .layout {
      width: 100%;
      max-width: 620px;
      display: flex;
      flex-direction: row;
      align-items: center;
      justify-content: space-between;
      gap: 16px;
    }
    @media (max-width: 500px) {
      .layout {
        flex-direction: column;
        gap: 10px;
      }
    }
    /* Left Panel: Equation Cards */
    .cards-col {
      flex: 1;
      display: flex;
      flex-direction: column;
      gap: 10px;
      width: 100%;
    }
    .eq-card {
      padding: 10px 12px;
      border-radius: 8px;
      cursor: pointer;
      user-select: none;
      transition: background-color 0.2s ease, box-shadow 0.2s ease, opacity 0.2s ease;
      background: #ffffff;
      border: 1.5px solid transparent;
      box-shadow: 0 1px 4px rgba(0,0,0,0.05);
    }
    .eq-card.linear {
      border-color: rgba(37, 99, 235, 0.35);
    }
    .eq-card.linear.active {
      background: #eff6ff;
      border-color: #2563eb;
      box-shadow: 0 0 0 1px #2563eb, 0 2px 8px rgba(37, 99, 235, 0.15);
    }
    .eq-card.quad {
      border-color: rgba(225, 29, 72, 0.35);
    }
    .eq-card.quad.active {
      background: #fff1f2;
      border-color: #e11d48;
      box-shadow: 0 0 0 1px #e11d48, 0 2px 8px rgba(225, 29, 72, 0.15);
    }
    .eq-card.sol-card {
      border-color: rgba(16, 185, 129, 0.35);
    }
    .eq-card.sol-card.active {
      background: #ecfdf5;
      border-color: #10b981;
      box-shadow: 0 0 0 1px #10b981, 0 2px 8px rgba(16, 185, 129, 0.15);
    }
    .eq-title {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      display: flex;
      align-items: center;
      gap: 6px;
      margin-bottom: 2px;
    }
    .linear .eq-title { color: #2563eb; }
    .quad .eq-title { color: #e11d48; }
    .sol-card .eq-title { color: #059669; }

    .eq-math {
      font-size: 15px;
      font-weight: 600;
      font-family: "Cambria Math", "Times New Roman", serif;
      color: #1e2945;
    }

    /* Right Panel: Coordinate Plane */
    .graph-container {
      flex: 1.2;
      width: 100%;
      background: #ffffff;
      border-radius: 10px;
      border: 1px solid #e2e8f0;
      box-shadow: 0 2px 8px rgba(0,0,0,0.04);
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }
    svg {
      width: 100%;
      height: auto;
      max-height: 250px;
      overflow: visible;
    }

    /* SVG Interactive Styling */
    .laser-line {
      stroke: #2563eb;
      stroke-width: 2.5;
      stroke-linecap: round;
      transition: stroke-width 0.2s ease, opacity 0.2s ease;
    }
    .parabola-path {
      stroke: #e11d48;
      stroke-width: 2.5;
      stroke-dasharray: 4 3;
      stroke-linecap: round;
      fill: none;
      transition: stroke-width 0.2s ease, opacity 0.2s ease;
    }
    .glow-point {
      fill: #10b981;
      stroke: #ffffff;
      stroke-width: 2;
      cursor: pointer;
      transition: r 0.2s ease, fill 0.2s ease;
    }
    .glow-ring {
      fill: none;
      stroke: #10b981;
      stroke-width: 1.5;
      opacity: 0.6;
      animation: pulse 2.4s infinite ease-in-out;
    }
    @keyframes pulse {
      0%, 100% { r: 5px; opacity: 0.7; }
      50% { r: 9px; opacity: 0.15; }
    }
    .grid-line {
      stroke: #f1f5f9;
      stroke-width: 1;
    }
    .axis {
      stroke: #94a3b8;
      stroke-width: 1.2;
    }
    .axis-label {
      font-size: 10px;
      fill: #64748b;
      font-family: system-ui, sans-serif;
    }
    .graph-label {
      font-size: 11px;
      font-weight: 600;
      font-family: system-ui, sans-serif;
      pointer-events: none;
    }
    .dimmed {
      opacity: 0.25 !important;
    }
    .highlighted {
      stroke-width: 3.5 !important;
    }
  </style>
</head>
<body>

  <div class="layout">
    
    <div class="cards-col">
      <div class="eq-card linear active" id="cardLinear" onclick="toggleFocus('linear')">
        <div class="eq-title">Line (Degree 1)</div>
        <div class="eq-math">y = x + 1</div>
      </div>

      <div class="eq-card quad active" id="cardQuad" onclick="toggleFocus('quad')">
        <div class="eq-title">Parabola (Degree 2)</div>
        <div class="eq-math">y = -x² + 4x</div>
      </div>

      <div class="eq-card sol-card active" id="cardSol" onclick="toggleFocus('both')">
        <div class="eq-title">2 Solutions (x, y)</div>
        <div class="eq-math">Intersections</div>
      </div>
    </div>

    
    <div class="graph-container">
      <svg viewBox="-30 -20 280 230" id="graphSvg">
        
        <defs>
          <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse">
            <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#f1f5f9" stroke-width="1"/>
          </pattern>
        </defs>
        <rect x="0" y="0" width="220" height="180" fill="url(#grid)" />

        
        <line x1="0" y1="180" x2="230" y2="180" class="axis" />
        <polygon points="230,177 236,180 230,183" fill="#94a3b8" />
        <line x1="0" y1="180" x2="0" y2="-10" class="axis" />
        <polygon points="-3,-10 0,-16 3,-10" fill="#94a3b8" />
        
        <text x="228" y="196" class="axis-label">x</text>
        <text x="-14" y="-4" class="axis-label">y</text>
        <text x="-8" y="194" class="axis-label">0</text>

        
        <path id="parabolaPath" class="parabola-path" />
        <line id="laserLine" class="laser-line" />

        
        <circle id="ring1" class="glow-ring" />
        <circle id="point1" class="glow-point" r="4.5" />

        
        <circle id="ring2" class="glow-ring" />
        <circle id="point2" class="glow-point" r="4.5" />

        
        <text x="75" y="16" fill="#e11d48" class="graph-label" id="lblQuad">y = ax² + bx + c</text>
        <text x="145" y="65" fill="#2563eb" class="graph-label" id="lblLinear">y = mx + b</text>
        <text x="135" y="105" fill="#059669" class="graph-label" id="lblSol">(x, y)</text>
      </svg>
    </div>
  </div>

  <script>
    // Coordinate Mapping:
    // Math Box: x in [-0.5, 4.5], y in [-0.5, 4.5]
    // SVG Box: width 220, height 180 (origin at (0, 180))
    // scale: 40 px per unit.
    // SVG_X = x * 40; SVG_Y = 180 - y * 40;
    function toSvg(x, y) {
      return {
        x: x * 40,
        y: 180 - (y * 40)
      };
    }

    // 1. Draw Parabola: y = -x^2 + 4x from x = -0.2 to 4.2
    let pD = "";
    for (let x = -0.2; x <= 4.25; x += 0.05) {
      const y = - (x * x) + 4 * x;
      const pt = toSvg(x, y);
      pD += (pD === "" ? "M " : " L ") + pt.x.toFixed(1) + " " + pt.y.toFixed(1);
    }
    document.getElementById('parabolaPath').setAttribute('d', pD);

    // 2. Draw Line: y = x + 1 from x = -0.3 to 3.8
    const lineStart = toSvg(-0.3, -0.3 + 1);
    const lineEnd = toSvg(3.6, 3.6 + 1);
    const laser = document.getElementById('laserLine');
    laser.setAttribute('x1', lineStart.x);
    laser.setAttribute('y1', lineStart.y);
    laser.setAttribute('x2', lineEnd.x);
    laser.setAttribute('y2', lineEnd.y);

    // 3. Exact Intersections:
    // -x^2 + 4x = x + 1  => x^2 - 3x + 1 = 0
    // x = (3 +- sqrt(5)) / 2
    const x1 = (3 - Math.sqrt(5)) / 2; // ~0.382
    const y1 = x1 + 1;                 // ~1.382
    const x2 = (3 + Math.sqrt(5)) / 2; // ~2.618
    const y2 = x2 + 1;                 // ~3.618

    const pt1 = toSvg(x1, y1);
    const pt2 = toSvg(x2, y2);

    const p1 = document.getElementById('point1');
    const r1 = document.getElementById('ring1');
    p1.setAttribute('cx', pt1.x);
    p1.setAttribute('cy', pt1.y);
    r1.setAttribute('cx', pt1.x);
    r1.setAttribute('cy', pt1.y);

    const p2 = document.getElementById('point2');
    const r2 = document.getElementById('ring2');
    p2.setAttribute('cx', pt2.x);
    p2.setAttribute('cy', pt2.y);
    r2.setAttribute('cx', pt2.x);
    r2.setAttribute('cy', pt2.y);

    // Interactive focus helper
    let currentMode = 'all';
    function toggleFocus(mode) {
      if (currentMode === mode) {
        mode = 'all';
      }
      currentMode = mode;

      const cLinear = document.getElementById('cardLinear');
      const cQuad = document.getElementById('cardQuad');
      const cSol = document.getElementById('cardSol');

      const pathQuad = document.getElementById('parabolaPath');
      const lineEl = document.getElementById('laserLine');
      const pts = [p1, p2, r1, r2];
      const lblLinear = document.getElementById('lblLinear');
      const lblQuad = document.getElementById('lblQuad');
      const lblSol = document.getElementById('lblSol');

      // Reset
      cLinear.classList.remove('active');
      cQuad.classList.remove('active');
      cSol.classList.remove('active');

      pathQuad.classList.remove('dimmed', 'highlighted');
      lineEl.classList.remove('dimmed', 'highlighted');
      pts.forEach(p => p.classList.remove('dimmed'));
      lblLinear.classList.remove('dimmed');
      lblQuad.classList.remove('dimmed');
      lblSol.classList.remove('dimmed');

      if (mode === 'linear') {
        cLinear.classList.add('active');
        lineEl.classList.add('highlighted');
        pathQuad.classList.add('dimmed');
        pts.forEach(p => p.classList.add('dimmed'));
        lblQuad.classList.add('dimmed');
        lblSol.classList.add('dimmed');
      } else if (mode === 'quad') {
        cQuad.classList.add('active');
        pathQuad.classList.add('highlighted');
        lineEl.classList.add('dimmed');
        pts.forEach(p => p.classList.add('dimmed'));
        lblLinear.classList.add('dimmed');
        lblSol.classList.add('dimmed');
      } else {
        // all active
        cLinear.classList.add('active');
        cQuad.classList.add('active');
        cSol.classList.add('active');
      }
    }
  </script>
</body>
</html>

HSA.REI.C.7

Aligned learning resources

Related diagrams