Chapter 1.4, Problem 27E

To determine

Tocompare:The graph of given function with the graph of parent its function.

Answer to Problem 27E

The function $y=x^2-12$ is obtained by shifting the parent function $y=x^2$ through a distance 12 units along -y axis (down).

Explanation of Solution

Given information:

The given function is $y=x^2-12$ .

Concept used:

A parent function is the simplest function of a family of functions. The family of the quadratic function $y=a{x}^2+bx+c$ has the simplest form function $y=x^2$ that is the parent function of this family of functions.

Transformations of Parent Functions:

The parent function $f\left(x\right)$ can be transformed in certain way .For, example: shift graphs up, down, left, and right.

Vertical Shifts: $f\left(x\right)+c$ moves up, $f\left(x\right)-c$ moves down.

Horizontal Shifts: $f\left(x+c\right)$ moves left, $f\left(x-c\right)$ moves right.

Graph:

The given function is

  $y=x^2-12$........(1)

Let $y=f\left(x\right)$ be the parent function of function of the opening up parabola $y=x^2-12$ .

Now, the parent function is movesleft by extent c. Then the transformed function (given function) is

  $y=f\left(x\right)-c$........(2)

Comparing results (1) and (2), $y=x^2$ is parent function, and $y=x^2-12$ is the transformed function.

The graphs of functions $y=x^2-12$ and $y=x^2$ are shown in Figure-1 here.

  

Comparison:

The function $y=x^2-12$ is obtained by shifting the parent function $y=x^2$ through a distance 12 units along -y axis (down).

Conclusion:

The function $y=x^2-12$ is obtained by shifting the parent function $y=x^2$ through a distance 12 units along -y axis (down).