Question

The function g(x) = 2x2 – 28x + 3 written in vertex form is g(x) = 2(x – 7)2 – 95. Which is one of the transformations applied to the graph of f(x) = x2 to produce the graph of g(x) = 2x2 – 28x + 3?

shifted up 3 units
shifted left 7 units
shifted right 7 units
shifted down 3 units

Answer 1

The vertex form tells us the answer. This is the general vertex form a parabola:
y = a(x-h)^2 + k

a indicates any stretching or shrinking
h indicates any shifting to the left (if h is positive) or the right (if h is negative)
k indicates any shifting up (if k is positive) or down (if k is negative)

Therefore, the transformation that apply is only
shifted right 7 units

Answer 2

The function
`g(x) = 2x^2 - 28x + 3` written in vertex form is
`g(x) = 2(x - 7)^2 - 95.`

You have to do such transformation to obtain the graph of the function g(x) from the graph of the function f(x) (the graph of f(x) is red on the diagram below):

1. translate graph of the function y=f(x) right 7 units to get graph of the function
`f_1(x)=(x-7)^2` (blue curve);

2. shrink twice in y-direction the graph of
`f_1(x)` to obtain the graph of the function
`f_2(x)=2(x-7)^2` (green curve);

3. translate graph of the function
`f_2(x)` down 95 units to get the graph of the function
`y=g(x)=2(x-7)^2-95` (orange curve).

From these steps the only possible choice of transformations is C - shifted right 7 units.