Horizontal levels and root symmetry

Horizontal levels and root symmetry

Secondary 2
14 marks
TGM Original Questions

Optional extension

    1. Complete the missing table values \(a,b,c\) for \(y=2x^2-4x-6\)[2]
    2. draw it for \(-2\le x\le4\).[2]
    1. Draw \(y=4\)[2]
    2. solve \(2x^2-4x-6=4\).[2]
  3. Explain why \(2x^2-4x-6=-9\) has no real solution.[2]
    1. State the symmetry line[2]
    2. if roots of \(2x^2-4x-6=k\) are \(p,q\), express \(p\) in terms of \(q\).[2]
\(x\)-\(2\)-\(1\)\(0\)\(1\)\(2\)\(3\)\(4\)
\(y\)\(a\)\(0\)-\(6\)\(b\)-\(6\)\(0\)\(c\)

For graph readings, give values to the nearest 0.1 unit where an exact value cannot be read from the grid. Use the labelled axes and grid provided.

Solution:

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Answer:(a)(i) \(a=10,b=-8,c=10\) (b)(ii) \(x=1\pm\sqrt6\approx-1.4,3.4\) (c) minimum is \(-8\) (d)(i) \(x=1\) (ii) \(p=2-q\).

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