One zero of a parabola is −10, and the other zero is 18 more than the first. What is the axis of symmetry?
Answer and explanation
Correct answer: x = −1
For a parabola with two real zeroes, the vertical axis of symmetry passes midway between the two x-intercepts. The first zero is −10. The second zero is 18 more than −10, so it is −10 + 18 = 8. The midpoint of the two zeroes is (−10 + 8)/2 = −2/2 = −1. Hence the axis of symmetry is x = −1, so option A is correct. The value x = 8 is the second zero itself, not the midpoint. The values x = 1 and x = −8 do not give the average of the two intercepts and therefore cannot represent the symmetry axis.
Frequently asked questions
What is the correct answer to this question?
x = −1
Why is this the correct answer?
For a parabola with two real zeroes, the vertical axis of symmetry passes midway between the two x-intercepts. The first zero is −10. The second zero is 18 more than −10, so it is −10 + 18 = 8. The midpoint of the two zeroes is (−10 + 8)/2 = −2/2 = −1. Hence the axis of symmetry is x = −1, so option A is correct. The value x = 8 is the second zero itself, not the midpoint. The values x = 1 and x = −8 do not give the average of the two intercepts and therefore cannot represent the symmetry axis.
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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