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Graphs of quadratic functions

Graphs of quadratic functions

Secondary 2

The sketch shows the graph of \(y=x^2-6x+5\). It cuts the \(x\)-axis at \(A\) and \(B\) and the \(y\)-axis at \(C\). \(T\) is the minimum point. The sketch is not drawn to scale.

  1. Find the coordinates of \(A\), \(B\) and \(C\).
  2. Write down the equation of the line of symmetry and find the coordinates of \(T\).
  3. Find the values of \(x\) for which \(y=12\).
  4. Explain why the equation \(x^2-6x+5=-5\) has no solution.

Solution:

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Answer:(a) \(A=(1,0)\), \(B=(5,0)\), \(C=(0,5)\) (b) \(x=3\); \(T=(3,-4)\) (c) \(x=-1\) or \(x=7\) (d) The least value of \(y\) is \(-4\), which is greater than \(-5\)

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