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A parabola intersects the -axis at and .What is the -coordinate of the parabola's vertex?
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Q. A parabola intersects the -axis at and .What is the -coordinate of the parabola's vertex?
- Identify Parabola Roots: The -coordinates where the parabola intersects the -axis are the roots of the parabola. For a parabola in standard form, , the -coordinate of the vertex can be found using the formula . However, we do not have the coefficients , , and . Instead, we can use the fact that the vertex of a parabola is exactly in the middle of the two -intercepts for a vertical parabola.
- Calculate Vertex X-coordinate: Calculate the midpoint between the two x-intercepts to find the x-coordinate of the vertex. The midpoint formula is , where and are the x-intercepts.
- Find Midpoint: Substitute the given x-intercepts into the midpoint formula: .
- Perform Calculation: Perform the calculation: .
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