Chapter 8, Problem 5CR

To determine

To identify: The characteristicof the quadratic function of the graph.

Explanation of Solution

Given information:

The graph of the quadratic function is shown below in Figure 1.

  

Figure 1

The behavior of the graph of the parabola is U shaped curve where axis of symmetry can be drawn through the vertex of parabola.

The vertex form of the parabola is $a{\left(x-h\right)}^2+k$ where the point $\left(h,k\right)$ is the vertex.

The value of $a$ tell the behavior of the graph. If the value of a is positive then the curve opens upward and if the value of a is negative then the curve opens downward.

It can be seen from the graph that the curve opens upward that means the value of $a$ must be positive and the vertex is $\left(1,-3\right)$ with the symmetry of $x=1$ .

The domain of the quadratic polynomial is always the set of real numbers that means the domain of the given graph is also the set of real numbers.

The range of the functions are the output values of the function.

It can be observed from the graph that the lowest value of the function is $-3$ and function approaches infinity.

Therefore, the range of the function is $\left[-3,\infty \right)$ .