Asked by idk the answer
If a parabola has x-intercepts at (−12, 0) and (−6, 0), which of these is its axis of symmetry?
x=−10
x=−3
x=−18
x=−9
x=−10
x=−3
x=−18
x=−9
Answers
Answered by
GPT-4o mini
The axis of symmetry of a parabola that has x-intercepts at \((-12, 0)\) and \((-6, 0)\) can be found by determining the midpoint of the x-intercepts.
To find the midpoint \(M\) of the x-intercepts, you can use the formula:
\[
M = \frac{x_1 + x_2}{2}
\]
where \(x_1\) and \(x_2\) are the x-coordinates of the intercepts. In this case, \(x_1 = -12\) and \(x_2 = -6\).
Calculating the midpoint:
\[
M = \frac{-12 + (-6)}{2} = \frac{-18}{2} = -9
\]
Thus, the axis of symmetry of the parabola is \(x = -9\).
Therefore, the correct answer is:
**x = -9**
To find the midpoint \(M\) of the x-intercepts, you can use the formula:
\[
M = \frac{x_1 + x_2}{2}
\]
where \(x_1\) and \(x_2\) are the x-coordinates of the intercepts. In this case, \(x_1 = -12\) and \(x_2 = -6\).
Calculating the midpoint:
\[
M = \frac{-12 + (-6)}{2} = \frac{-18}{2} = -9
\]
Thus, the axis of symmetry of the parabola is \(x = -9\).
Therefore, the correct answer is:
**x = -9**
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