Horizontal levels and root symmetry
Horizontal levels and root symmetry
Secondary 2
14 marks
TGM Original Questions
Optional extension
- Complete the missing table values \(a,b,c\) for \(y=2x^2-4x-6\)[2]
- draw it for \(-2\le x\le4\).[2]
- Draw \(y=4\)[2]
- solve \(2x^2-4x-6=4\).[2]
- Explain why \(2x^2-4x-6=-9\) has no real solution.[2]
- State the symmetry line[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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