Suppose you are given a parabola with two points that have the same y-value, such as (-7, 11) and (3, 11). Explain how to find the equation of the axis of symmetry for this parabola, and then determine that equation.

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02-09-2022
Mathematics

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Suppose you are given a parabola with two points that have the same y-value, such as (-7, 11) and (3, 11). Explain how to find the equation of the axis of symmetry for this parabola, and then determine that equation.

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xero099 xero099 · Answer 1 · 2022-09-06T10:35:14-04:00

By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.

How to derive the equation of the axis of symmetry

In this question we know the locations of two points with the same y-value, which means that the axis of symmetry is parallel to the y-axis and that both points are equidistant. Thus, the axis of symmetry passes through the midpoint of the line segment whose ends are those points.

First, calculate the coordinates of the midpoint by the midpoint formula:

M(x, y) = 0.5 · (- 7, 11) + 0.5 · (3, 11)

M(x, y) = (- 2, 11)

Second, look for the first coordinate of the midpoint and derive the equation of the line associated with the axis of symmetry:

x = - 2

By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.

To learn more on axes of symmetry: https://brainly.com/question/11957987

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