16Hit1600
Advanced MathHardAxis of symmetry from the x-intercepts

Advanced Math practice question

The graph of f(x) = x² − 6x + 5 in the xy-plane crosses the x-axis at two points. What is the equation of the graph's axis of symmetry?

  1. A. x = 3Correct
  2. B. x = 1
  3. C. x = 5
  4. D. x = −3

Answer: A. x = 3

The x-intercepts are 1 and 5 (since x² − 6x + 5 = (x − 1)(x − 5)); the axis is midway, x = 3. (Also −b/2a = 6/2 = 3.)

Why the other answers are wrong

B. x = 1
x = 1 is one intercept, not the midpoint.
C. x = 5
x = 5 is the other intercept.
D. x = −3
x = −3 has the wrong sign; −b/2a = −(−6)/2 = 3.

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