To determine the equation of a curved line going downward that passes through the point (-3, 0), we need the context of the type of curve we're dealing with. Common types of curved lines include quadratic functions, exponential functions, and logarithmic functions.
Since the point given is (-3, 0), it suggests that the curve intersects the x-axis at that point. A downward-opening parabola can be given in the vertex form: \[ y = a(x - h)^2 + k \] where \((h, k)\) is the vertex of the parabola and \(a\) determines the direction and the width of the parabola.
Assuming the vertex of the parabola is above the x-axis, it would be something like: \[ y = a(x + 3)^2 + k \] Given that the curve is going downward, \(a\) should be negative.
We can also have other forms such as:
- A simple quadratic function like \( y = ax^2 + bx + c \)
- Exponential decay, if the curve is dropping sharply.
However, we need more information to derive an exact equation. For example, if we knew the curvature behavior, or other points on the curve, it would help.
As an example of a downward-opening parabola that passes through (-3, 0), we could assume the simplest case where the vertex is at (-3, k) for some positive \(k\): \[ y = -a(x + 3)^2 + k \]
Alternatively, you could use \(y = -x^2 - 6x - 9\) which factors nicely at x = -3 but not as elegant as it is not technically in standard form.
Please provide more details or points on the graph for a more accurate equation.
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