In a vertical parabola, which parameter should equal zero?

In a vertical parabola, which parameter should equal zero?

• A. c
• B. a
• C. b
• D. d

Answer: (C)

In the context of a vertical parabola, the standard form of its equation is typically expressed as \(y = ax^2 + bx + c\). Here, \(a\), \(b\), and \(c\) are coefficients that determine the shape and position of the parabola. In this formulation, the parameter \(b\) relates to the linear component of the equation. Specifically, when \(b\) equals zero, the parabola opens symmetrically around the y-axis, making the vertex positioned directly on the y-axis. This characteristic is essential to identify since it simplifies the parabola's analysis and graphing. Therefore, if you want a vertical parabola that is symmetrical about the y-axis, you need to set \(b\) to zero. By doing so, the equation simplifies to \(y = ax^2 + c\), where the vertex can be easily identified and drawn. This clearly illustrates why the value of \(b\) should be zero for a symmetric vertical parabola.

In the context of a vertical parabola, the standard form of its equation is typically expressed as (y = ax^2 + bx + c). Here, (a), (b), and (c) are coefficients that determine the shape and position of the parabola.

In this formulation, the parameter (b) relates to the linear component of the equation. Specifically, when (b) equals zero, the parabola opens symmetrically around the y-axis, making the vertex positioned directly on the y-axis. This characteristic is essential to identify since it simplifies the parabola's analysis and graphing.

Therefore, if you want a vertical parabola that is symmetrical about the y-axis, you need to set (b) to zero. By doing so, the equation simplifies to (y = ax^2 + c), where the vertex can be easily identified and drawn. This clearly illustrates why the value of (b) should be zero for a symmetric vertical parabola.