Reading and transforming a quadratic graph

Reading and transforming a quadratic graph

Secondary 2
14 marks
TGM Original Questions

Optional extension

The graph shown is \(y=x^2-6x-7\).

  1. Find
    1. \(y\) when \(x=2\),[2]
    2. its intercepts on the \(x\)-axis, and[2]
    3. the coordinates of its turning point \(T\).[2]
  2. Sketch, with key features,
    1. \(y=-x^2-6x-7\), and[2]
    2. \(y=x^2\).[2]
  3. Another quadratic \(y=ax^2+bx+c\) passes through \((0,0),(4,0),(-2,24)\).
    1. Find \(c\).[2]
    2. Find \(a\) and \(b\).[2]

Solution:

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Answer:(a)(i) \(-15\) (ii) \((-1,0),(7,0)\) (iii) \(T=(3,-16)\). (b)(i) vertex \((-3,2)\), symmetry \(x=-3\), opens downward (ii) vertex \((0,0)\), touches the \(x\)-axis. (c)(i) \(c=0\) (ii) \(a=2,b=-8\).

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