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Grade 11 · Functions and Graphs
The Parabola: y = a(x + p)² + q (Grade 11)
MEMORANDUM
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  / 14

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Write down the turning point of y = 2(x + 2)² − 8.
    (1)
    (−2 ; −8)✓ (1)
  2. 2
    Determine the x-intercepts of y = 2(x + 2)² − 8.
    (3)
    (x + 2)² = 4 → x + 2 = ±2 → x = 0 or x = −4✓✓✓ (3)
  3. 3
    Determine the y-intercept of y = 2(x + 2)² − 8.
    (2)
    x = 0 → y = 8 − 8 = 0✓✓ (2)
  4. 4
    Write down the equation of the axis of symmetry of y = 2(x + 2)² − 8.
    (1)
    x = −2✓ (1)
  5. 5
    Write down the range of y = 2(x + 2)² − 8.
    (1)
    y ≥ −8✓ (1)
  6. 6
    Write down the domain of y = 2(x + 2)² − 8.
    (1)
    x ∈ ℝ✓ (1)
  7. 7
    Write y = x² − 6x + 5 in the form y = a(x + p)² + q.
    (3)
    y = (x − 3)² − 4✓✓✓ (3)
  8. 8
    For what values of x is y = 2(x + 2)² − 8 increasing?
    (2)
    xyy = 2(x + 2)² − 8TP (−2 ; −8)(−4 ; 0)(0 ; 0)−6−5−4−3−2−1123−10−8−6−4−224
    To the right of the turning point: x > −2✓✓ (2)
TOTAL: 14 marks
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