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?
- A. x = 3Correct
- B. x = 1
- C. x = 5
- 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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