Suppose the graph of y = x2 is shifted. What is the equation of the function, g(x) ?

Answer 1

The graph is shifted to which direction? by how many units?
Generally speaking,
y-k = (x-h)^2 will shift y = x^2 vertically by k units and horizontally by h units.

Answer 2

If the graph is shifted vertically, this is in the y direction, so you need to add a value, b, that denotes it was shifted b units in the y direction. This means you need to add a units to y or...
y + b = x^2
so g(x) = x^2 - b

If the graph is shifted in the horizontal direction, this means you need to add b to x, but you have to make sure to add it to *only* x, and not the x^2 factor, so
g(x) = (x+b)^2 or
g(x) = x^2 + 2bx + b^2

Note: b can be positive or negative. Positive denotes a shift in the positive y or x direction.

Answer 3

You didn't mention whether it was shifted up or down, and by how many unit.
If the graph was shifted up 3 units, the equation will be y=2x+3
If the graph was shifted down 3 units, the equation will be y=2x-3

Answer 4

Suppose y = f(x) = x²
Let g(x) = x² + 3
g(x) is obtained from graph of f(x) by translation of 3 upwards.
Similarly h(x) = x² - 4 is obtained from graph of f(x) by a translation of 4 downwards.

Answer 5

If f(x) is shifted in x by an amount a, then

g(x) = f(x+a) = (x+a)^2 = x^2 + 2ax + a^2

Answer 6

Sounds like you have

f(x) = x^2

and you want

g(x) = f(x shifted).

What's x shifted?
It's

x - a

if x is shifted left by a
(which will be a shift to the right
if a < 0).

So

g(x)
= f(x shifted)
= f(x - a).

Since f squares its argument,

f(x - a)
= (x - a)^2
= x^2 - 2ax + a^2;

and that's g(x).

Answer 7

let the graph is shifted upto t then
g(X)=(x+t)*2