negative parabola
Opens down and has a maximum.
A negative parabola is a type of quadratic function in which the highest power of the variable is 2 and the coefficient of the variable term is negative. The graph of a negative parabola is a downward-facing curve that opens downwards.
The general formula for a negative parabola is given by:
y = ax^2 + bx + c
where a is a negative constant and b and c are constants. The vertex form of the equation of a negative parabola is:
y = a(x – h)^2 + k
where (h, k) is the vertex of the parabola. In this form, we can easily identify the vertex and the orientation of the parabola. Since the coefficient of the squared term is negative, the parabola opens downwards.
The x-intercepts of a negative parabola are given by:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
These are the solutions to the equation y = 0, which represents the points where the parabola intersects the x-axis.
Applications of negative parabolas can be found in physics, economics, and engineering, among others. For example, the path of a projectile launched from a height can be modeled by a negative parabola, as can the profit function for a company that experiences diminishing returns.
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