Asked by void
Given 2 solutions, (-4,12) and (6,12), what is the axis of symmetry? How do you know? Explain your thinking mathematically.
Answers
Answered by
mathhelper
Poorly worded question.
The term "axis of symmetry" is usually associated with a parabola, so
I will assume you have two points on this parabola.
From the two equal values of y = 12, the axis of symmetry would be the
right bisector of the segment joining your two points,
that would be x = 1 , (notice the x of their midpoint is 1)
( the equation could be y = a(x-1)^2 + k
(6,12) lies on it, so 12 = a(25) + k
(-4,12) lies on it, so 12 = a(25) + k , same equation, so we don't have enough information to find a unique solution.
could be ....
let k = 11, 12 - 11 = a(25), a = 1/25
y = (1/25)(x-1)^2 + 11
let k = -13 , 12 = a(25) - 13 , a = 1
y = (x-1)^2 - 13
etc
The term "axis of symmetry" is usually associated with a parabola, so
I will assume you have two points on this parabola.
From the two equal values of y = 12, the axis of symmetry would be the
right bisector of the segment joining your two points,
that would be x = 1 , (notice the x of their midpoint is 1)
( the equation could be y = a(x-1)^2 + k
(6,12) lies on it, so 12 = a(25) + k
(-4,12) lies on it, so 12 = a(25) + k , same equation, so we don't have enough information to find a unique solution.
could be ....
let k = 11, 12 - 11 = a(25), a = 1/25
y = (1/25)(x-1)^2 + 11
let k = -13 , 12 = a(25) - 13 , a = 1
y = (x-1)^2 - 13
etc
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