Question

What is the rang of y=-x^2-2x+3

Answer 1

Step-by-step explanation:

Looking at the function, we can see that the function is a parabola in shape

The general equation form of a parabola is:

`\text{ y = ax}^2\text{ + bx + c}`

if a is negative as we have seen, the parabola faces down

Now, to find the range, which is the possible f(x) values, we need to get the vertex of the parabola

The range of values is simply between the lowest possible number and the vertex

We have the vertex of the parabola at the point (-1,4)

So, we have the range of values in:

`\begin{gathered} \text{ range} \\ f(x)\text{ }\leq\text{ 4} \\ \text{Interval notation:} \\ (-\infty,4\rbrack \end{gathered}`