Answer:
The function has a range of all real numbers less than or equal to 2.
Explanation:
Quadratic functions form parabolas, which look like a U-shape.
What is Range
Range describes the y-values covered by a function. So, the range contains every y-value that is a possible output of a function. You can find the range of a function from the graph by looking at what y-values are or will be covered by the function.
The range of a quadratic is always all real numbers greater than/less than the y-value of the vertex. Positive quadratics have ranges greater than the vertex, and negative quadratics have ranges less than the vertex.
Finding the Range
The parabola given is negative. We know this because the graph opens downward. This means that the graph has a maximum, and the range is less than the vertex.
By looking at the graph we can tell that eventually, the graph will cover all y-values under y-value 2. Note that 2 is the y-value of the vertex. So the range is all real values less than or equal to 2. This means that any number less than or equal to 2 is a possible output of the function.