Chapter 1.7, Problem 68E

(a)

To determine

To find: the method of graphing preferable to use for given function.

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=3x^2-4x+1$

Calculation:

Let us consider the function

  $f\left(x\right)=3x^2-4x+1$ ………..(1)

To draw the function represented by the equation (1), first we have to tabulate the values of $f\left(x\right)$ corresponding values of $x$ .

Then plot the points and join those points with free hand

Since it is a quadratic equation, it is in the shape of parabola

(b)

To determine

To find: the method of graphing do you prefer to use for given function.

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=2{\left(x-1\right)}^2-6$

Calculation:

Let us consider the function

  $f\left(x\right)=2{\left(x-1\right)}^2-6$ ……………(2)

To draw the function represented by the equation (1), by using the method of translating a parent function $y=x^2$

We can obtain the graph of the function represented by (1) by using the following translations

First shift the graph of $h\left(x\right)=2{\left(x-1\right)}^2-6$ unit to the right. And then stretch the graph by multiplying functional values by 2, and then shift the graph 6 units down wards.