Final answer:
The range of the quadratic equation is y < 4. Hence the correct answer is option C
Step-by-step explanation:
The range of a quadratic equation can be determined by analyzing the vertex of the parabola.
In the equation y = -x^2 - 2x + 3, the coefficient of x^2 is negative, indicating that the parabola opens downward. Therefore, the vertex represents the maximum point of the parabola.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a. In this case, a = -1 and b = -2. Substituting these values, we have x = -(-2)/(2*(-1)) = 1.
Substituting x = 1 into the equation, we can find the y-coordinate of the vertex: y = -(1^2) - 2(1) + 3 = 0.
Since the vertex has coordinates (1, 0), the range of the equation is all y-values less than or equal to 0.
Therefore, the correct answer is option C) y < 4.