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Titik balik fungsi kuadrat

Aljabar Matematika · SMA medium

Koordinat titik balik fungsi kuadrat 4y−4x2+4x−7=04y - 4x^2 + 4x - 7 = 0 adalah....

  1. A
    (−12,32)\left(-\tfrac12, \tfrac32\right)
  2. B
    (−12,74)\left(-\tfrac12, \tfrac74\right)
  3. C
    (12,−32)\left(\tfrac12, -\tfrac32\right)
  4. D
    (12,32)\left(\tfrac12, \tfrac32\right)
    ✓
  5. E
    (12,74)\left(\tfrac12, \tfrac74\right)

Kunci jawaban

D

Penjelasan singkat

y=x2−x+74y = x^2 - x + \tfrac74; titik balik x=12x=\tfrac12, y=32y=\tfrac32.

(Jawaban dihitung & diverifikasi dengan Python/SymPy.)

4y=4x2−4x+7⇒y=x2−x+744y=4x^2-4x+7 \Rightarrow y=x^2-x+\tfrac74. Titik balik pada x=−b2a=12x=-\dfrac{b}{2a}=\dfrac12, dengan y=(12)2−12+74=14−12+74=32y=\left(\tfrac12\right)^2-\tfrac12+\tfrac74=\tfrac14-\tfrac12+\tfrac74=\tfrac32. Jadi (12,32)\left(\tfrac12,\tfrac32\right) → D.

⚡ Latihan Matematika SMA