Question

Consider the following function.
f(x) = x2 - 5x
(a) Give the function g(x) whose graph could be obtained by shifting the graph of f(x) by 4 units to the right.

g(x)=

Answer 1

and just to clarify the function is f(x)= x^2 - 5x

Answer 2

first complete the square

Answer 3

y= (x -(5/2) )^2 - (25/4)

Answer 4

now shifting along the horizontal axis is done by adding or substracting something inside the bracket.

Currently the vertex is ( (5/2) , (-25/4) )

we want to shift it to the right , ie make the x value of the vertex more positive, so inside the bracket you subtract the number by which you want to shift

so subtract 4 inside the brackets


therefore y = ( x- (5/2) -4 ) ^2 -(25/4) = (x-(13/2) )^2 -(25/4)

Answer 5

you dont change the constant on the end, that shifts it up and down, you dont want that.

Answer 6

\[y= (x- \frac{13}{2})^2 -\frac{25}{4}\]

you can expand it if you want, but thats the answer