UPCAT Mathematics practice question 40: What is the vertex of the parabola y = x² − 6x + 5?
Correct answer
C. (3, −4)
The axis of symmetry is x = −b/(2a) = 6/2 = 3. Substituting gives y = 9 − 18 + 5 = −4.
The question
What is the vertex of the parabola y = x² − 6x + 5?
- Option A: (−3, 32)
- Option B: (3, 5)
- Option C: (3, −4)Correct
- Option D: (6, 5)
Why C is correct
The axis of symmetry is x = −b/(2a) = 6/2 = 3. Substituting gives y = 9 − 18 + 5 = −4.
Why the other options are wrong
- A (−3, 32)
- Uses x = +b/(2a) and so gets the sign of the axis of symmetry wrong.
- B (3, 5)
- Finds the correct x but reads off the constant term instead of substituting to get y.
- D (6, 5)
- Takes the coefficients straight from the equation rather than computing anything.