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?
1)shifted up 3 units
2)shifted left 7 units
3)shifted right 7 units
4)shifted down 3 units

Answer 1

3)shifted right 7 units

Answer 2

Answer

3)shifted right 7 units

Explanation

Remember the translation rules:

$f(x)+b$ shifts the function b units upward

$f(x)-b$ shifts the function b units upward

$f(x+b)$ shifts the function b units to the left

$f(x-b)$ shifts the function b units to the right

From the vertex form: $g(x)=2(x-7)^2-92$,of our function, we can infer that:

The parent function $f(x)$ has been shifted 7 units to the right (look at the term $(x-7)^2$) and 91 units upward.

So we can conclude that the correct option is: 3)shifted right 7 units