Answer
a) Method of plotting points;
b) Method of translating the parent function
Work Step by Step
a) We are given the function:
$f(x)=3x^2-4x+1$
The parent function of $f$ is $f_0(x)=x^2$. In order to use the parent function, we must bring the equation to the form $f(x)=a(x-h)^2+k$, which is difficult as building a square leads to fractions. In this case it is better to use the method of plotting points.
b) We are given the function:
$f(x)=2(x-1)^2-6$
The function is in the form $f(x)=a(x-h)^2+k$, so we can graph it using transformations: a horizontal shift, a vertical stretch, and a vertical shift.
