Chapter 4.5, Problem 56E

(a)

To determine

To find: the real zeros of the function $f$ .

Answer to Problem 56E

The real zeros of functions are $x=-2$ and $x=1$ .

Explanation of Solution

Given information:

The information in the graph to answer the questions,

  

Calculation:

From the graph it is very clear that the graph crosses $x$ axis at $x=-2$ and $x=1$ .

Therefore, the real zeros of functions are $x=-2$ and $x=1$ .

(b)

To determine

To write: an equation of the quartic function in factored form.

Answer to Problem 56E

the polynomial function is $f\left(x\right)={\left(x+2\right)}^2{\left(x-1\right)}^2$ .

Explanation of Solution

Given information:

The information in the graph to answer the questions,

  

Calculation:

Because $x=-2$ and $x=1$ are zeros of function, so two factors are

  $x-\left(-2\right)=x+2$ and $x-\left(1\right)=x-1$

Because the graph touches $x$ axis at $x=-2$ and $x=1$ , so power of factor $x+2$ and $x-1$ must be 2.

Therefore, the polynomial function is $f\left(x\right)={\left(x+2\right)}^2{\left(x-1\right)}^2$ .