Given the \( x \)-intercepts of a parabola, write the equation of the line of symmetry. 20. \( x \)-intercepts: \( (-3,0) \) and \( (3,0) \) 21. \( x \)-intercepts: \( (-4,0) \) and \( (16,0) \) 22. \( x \)-intercepts: \( (-2,0) \) and \( (5,0) \) 23. \( x \)-intercepts: \( (-14,0) \) and \( (-3,0) \) 24. \( x \)-intercepts: \( (17,0) \) and \( (33,0) \) 25. \( x \)-intercepts: \( (-0.75,0) \) and \( (2.25,0) \)
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The line of symmetry of a parabola can be found by averaging the \( x \)-coordinates of the \( x \)-intercepts. This is because the line of symmetry is located exactly in the middle of the intercepts. For example, if the \( x \)-intercepts are \( (-3,0) \) and \( (3,0) \), you would calculate the average as follows: \(\frac{-3 + 3}{2} = 0\). Therefore, the equation of the line of symmetry is \( x = 0 \). For \( x \)-intercepts of \( (-4,0) \) and \( (16,0) \), calculate \(\frac{-4 + 16}{2} = 6\), resulting in the equation of the line of symmetry being \( x = 6 \). Just keep following this method, and you’ll quickly find those lines of symmetry!