To determine the equation of a curve that passes through the point (0, -3) and is described as a downward-curving line, we can start by considering a general downward-opening quadratic or cubic function.
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Quadratic Function: A simple form would be in the form of \( y = ax^2 + bx + c \), where \( a < 0 \) for the curve to open downward. Given the point (0, -3), we can substitute \( x = 0 \) and \( y = -3 \):
\[ -3 = a(0)^2 + b(0) + c \implies c = -3 \]
Thus, the equation becomes:
\[ y = ax^2 + bx - 3 \]
You would need additional points to determine \( a \) and \( b \).
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Cubic Function: Another option is a cubic function of the form \( y = ax^3 + bx^2 + cx + d \). Using the same substitution:
\[ -3 = d \implies d = -3 \]
Thus, the equation is:
\[ y = ax^3 + bx^2 + cx - 3 \]
Again, you would need more points or additional information about the shape or characteristics of the curve to uniquely determine the coefficients \( a, b, \) and \( c \).
If you have more specific characteristics or points of this curve, please provide them for a more precise equation!
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