The range of a quadratic function is the set of all real numbers less than or equal to 3. Which equations could represent the function?
Select TWO correct answers.
Let's assume the quadratic function is in the form of y = ax^2 + bx + c, where a, b, and c are constants.
To find the range of the quadratic function, we can consider its graph. Since the range is the set of all real numbers less than or equal to 3, this means that the graph of the quadratic function must be a downward-opening parabola with its vertex at the maximum value and y-coordinate being 3 or less.
Two possible equations for such a quadratic function could be:
1) y = -x^2 + 3
In this equation, the coefficient a is negative, indicating a downward-opening parabola. The vertex of the parabola is at (0, 3), which is a maximum point, and all y-values for this parabola will be equal to or less than 3.
2) y = -x^2 + 1
Similarly, in this equation, a is negative, indicating a downward-opening parabola. The vertex of the parabola is at (0, 1), which is a maximum point. All y-values for this parabola will be equal to or less than 1.
These two equations represent quadratic functions whose range is the set of all real numbers less than or equal to 3.