Hint
Use the stated units and precision. Set each given linear factor equal to zero.
Worked solution
(a)
The zero factors locate the two roots. Their average determines the symmetry line.
Answer: \(x=-4, 3\); \(\displaystyle x=- \frac{1}{2}\)
(b)
Set each given linear factor equal to zero.
The factor \(x - 3\) vanishes at 3.
Answer: \(3\)
(c)
Find the midpoint of the two root positions.
Average the two intercepts to obtain \(\displaystyle - \frac{1}{2}\).
Answer: \(\displaystyle - \frac{1}{2}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Read each zero factor to determine both roots.
- 1 mark: Average the two roots to determine the vertical symmetry line.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Set each given linear factor equal to zero.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Find the midpoint of the two root positions.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.