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.
A.) f(x) = (x - 2) ^2 + 3
B.) f(x) = -(x - 2)^2 + 3
C.) f(x) = -x^2 + 3
D.) f(x) = (x+ 3)^2 + 2
E.) f(x) = -(x + 3)^2 + 2
The range of a quadratic function can be determined by looking at the coefficient in front of the x^2 term.
The equation f(x) = (x - 2) ^2 + 3 has a positive coefficient in front of the x^2 term, so the graph of this function opens upwards and the range includes all real numbers greater than or equal to the vertex. Since the vertex of this function is (2, 3), the range of this function is all real numbers greater than or equal to 3.
The equation f(x) = -(x - 2)^2 + 3 has a negative coefficient in front of the x^2 term, so the graph of this function opens downwards and the range includes all real numbers less than or equal to the vertex. Since the vertex of this function is (2, 3), the range of this function is all real numbers less than or equal to 3.
Therefore, the correct equations are:
A.) f(x) = (x - 2) ^2 + 3
B.) f(x) = -(x - 2)^2 + 3