One zero of a parabola is -8, and the other zero is 12 more than the first. What is the axis of symmetry?
Answer and explanation
Correct answer: x = -2
For a parabola with two real zeroes r1 and r2, the axis of symmetry lies exactly midway between them, so its equation is x = (r1 + r2)/2. One zero is -8, and the other is 12 greater: -8 + 12 = 4. Thus the two zeroes are -8 and 4. Their midpoint is (-8 + 4)/2 = -4/2 = -2. Therefore the axis of symmetry is x = -2, making option A correct. Option C is the second zero itself, not the midpoint. Option D is the unhalved sum of the zeroes, and option B results from an incorrect sign or midpoint calculation.
Frequently asked questions
What is the correct answer to this question?
x = -2
Why is this the correct answer?
For a parabola with two real zeroes r1 and r2, the axis of symmetry lies exactly midway between them, so its equation is x = (r1 + r2)/2. One zero is -8, and the other is 12 greater: -8 + 12 = 4. Thus the two zeroes are -8 and 4. Their midpoint is (-8 + 4)/2 = -4/2 = -2. Therefore the axis of symmetry is x = -2, making option A correct. Option C is the second zero itself, not the midpoint. Option D is the unhalved sum of the zeroes, and option B results from an incorrect sign or midpoint calculation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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