Chapter 4.4, Problem 3MCQ

To determine

To find: whether the given function has a maximum value or minimum value. Hence to calculate the range and domain of the function.

Answer to Problem 3MCQ

The maximum value is $6$ . The range and domain are given below.

Explanation of Solution

Given:

The graph of the quadratic equation is:

  $f\left(x\right)=-x^2+2x+5$

The graph of the given function is as:

  

The quadratic equation $f\left(x\right)=a{x}^2+bx+c\text{wher}\text{}\text{e}\text{a}\ne \text{0}$ attains its maximum value when:

The graph is opens down & $a<0$ .

The maximum value is given by the $y$ -coordinate of the vertex.

As the graph opens down & $-1<0$ , so the above graph has maximum value.

The maximum value is $6$ .

The range and domain of the graph is calculated by using the graph as:

  $\begin{array}{c}\text{Domain}=\left\{x:x\text{is a real number}\right\}\\ \text{Range}=\left\{y:y\le 6\right\}\end{array}$