Graphs — O/L Mathematics

How do I practise Graphs?

1 question with a worked solution

1. What are the coordinates of the turning point (vertex) of the quadratic graph y = (x - 3)² - 4, and does it represent a minimum or maximum value?
   1. A) (-3, -4), minimum
   2. B) (3, 4), maximum
   3. C) (-3, 4), maximum
   4. D) (3, -4), minimum
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   Correct answer: D) (3, -4), minimum

   The vertex form of a parabola is y = a(x - h)² + k with turning point at (h, k). Here, h = 3, k = -4. Since a = 1 > 0, the parabola opens upwards and has a minimum at (3, -4).

   Show worked solution

   Step 1: Write in completed square form: y = (x - 3)² - 4. Step 2: Since (x - 3)² ≥ 0 for all real x, minimum y occurs when x - 3 = 0 → x = 3. Step 3: Minimum value of y = 0 - 4 = -4. Step 4: Coordinates of vertex = (3, -4); nature = minimum. Answer: (3, -4), minimum.
   Modelled on: the O/L Mathematics examination pattern

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Where does Graphs fit in the syllabus?

Grade 11 · Term 2