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Grade 10 · Functions
Sketching the Parabola: The Complete Exam Guide
MEMORANDUM
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Mark
  / 20

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
    For y = x2 − 4x + 3: shape, y-intercept, x-intercepts. (up)
    (2)
    a>0 → up; (0,3); (x−1)(x−3)=0 → x = 1, 3✓✓ (2)
  2. 2
    Turning point of y = x2 − 4x + 3. (up)
    (2)
    x = 42 = 2; y = 4−8+3 = −1 → (2, −1)✓✓ (2)
  3. 3
    For y = x2 + 6x + 5: x-intercepts. (up)
    (2)
    (x+1)(x+5)=0 → x = −1, −5✓✓ (2)
  4. 4
    Shape and turning point x of y = −2x2 + 8x − 6. (down)
    (2)
    a<0 → down; x = −8/(2·−2) = 2✓✓ (2)
  5. 5
    y-intercept of y = −x2 + 3x − 4. (down)
    (2)
    (0, −4)✓✓ (2)
  6. 6
    Does y = x2 + x + 4 cross the x-axis? (discriminant)
    (2)
    b2−4ac = 1−16 = −15 < 0 → No✓✓ (2)
  7. 7
    Turning point of y = x2 − 6x + 11 (no roots). (discriminant)
    (2)
    x = 3; y = 9−18+11 = 2 → (3, 2)✓✓ (2)
  8. 8
    Axis of symmetry of y = x2 − 8x + 7. (axis)
    (2)
    x = 82 = 4✓✓ (2)
  9. 9
    A parabola has roots 2 and 4 and passes through (0, 8). Find a. (from graph)
    (2)
    8 = a(0−2)(0−4) = 8a → a = 1✓✓ (2)
  10. 10
    Equation of a parabola with roots −2 and 5, a = 1. (from graph)
    (2)
    y = (x+2)(x−5) = x2 − 3x − 10✓✓ (2)
TOTAL: 20 marks
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