Question

A graph shows a curved line going downward. Its points are (0,-3.) what is the equation?

Answer 1

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.

1. **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 \( b \).

2. **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!