Advanced MathHardAxis of symmetry and minimum from factored form
Advanced Math practice question
The function q is defined by q(x) = (x − 5)(x + 1). Which statement is true about the graph of y = q(x)?
- A. Its axis of symmetry is x = 2 and its minimum value is −9.Correct
- B. Its axis of symmetry is x = 2 and its minimum value is −5.
- C. Its axis of symmetry is x = −2 and its minimum value is −9.
- D. Its axis of symmetry is x = 3 and its minimum value is −8.
Answer: A. Its axis of symmetry is x = 2 and its minimum value is −9.
The zeros are 5 and −1; the axis is their midpoint, x = 2. q(2) = (−3)(3) = −9.
Why the other answers are wrong
- B. Its axis of symmetry is x = 2 and its minimum value is −5.
- −5 is the y-intercept, q(0), not the minimum.
- C. Its axis of symmetry is x = −2 and its minimum value is −9.
- The midpoint of 5 and −1 is 2, not −2.
- D. Its axis of symmetry is x = 3 and its minimum value is −8.
- x = 3 is not midway between the zeros.
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