Pregunta
Question 5 The Axis of Symmetry is the equation of the Vertical Line the the vertex of the Parabola. 0.5 pts True Oalse
Ask by O'Quinn Martin. in the United States
Mar 18,2025
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The statement is true.
Solución
1. The vertex form of a parabola is given by
\[
y = a(x - h)^2 + k,
\]
where \((h, k)\) is the vertex.
2. The equation \(x = h\) represents the vertical line that passes through the vertex \((h, k)\). This vertical line is the axis of symmetry because it divides the parabola into two mirror-image halves.
3. Therefore, the statement "The Axis of Symmetry is the equation of the Vertical Line through the vertex of the Parabola" is true.
Answer: True.
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Simplifique esta solución The Deep Dive
True! The Axis of Symmetry for a parabola is indeed a vertical line that passes through the vertex. This means if you were to fold the parabola along this line, both halves would match perfectly. It can be calculated using the formula \(x = -\frac{b}{2a}\) for a parabola described by the equation \(y = ax^2 + bx + c\). In practical applications, understanding the Axis of Symmetry can help in fields such as architecture and engineering, where parabolic arcs are used for bridges and structures. Knowing where the symmetry lies ensures load distribution and aesthetic design are harmonious, contributing to the structural integrity and visual appeal!
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