Expert: Sherman D. - 2/9/2005

Question
suppose f(x)= x^2 - 3x

what 3 function would be obtained by shifting this graph

4 units to the right

3 units to the left

up 3 units  

Answer
f(x) = x^2 - 3x

shift right, just substitute (x - a) for x
shift left, just substitute (x + a) for x
shift up, x^2 - 3x becomes x^2 - 3x + b
shift down, x^2 - 3x becomes x^2 - 3x - b

4 units to the right
f(x) = (x - 4)^2 - 3(x - 4)
f(x) = ((x - 4)(x - 4)) - 3x + 12
f(x) = (x^2 - 4x - 4x + 16) - 3x + 12
f(x) = x^2 - 8x + 16 - 3x + 12
f(x) = x^2 - 11x + 28
thats if you were to right it all the way out

3 units to the left
f(x) = (x + 3)^2 - 3(x + 3)
f(x) = ((x + 3)(x + 3)) - 3x - 9
f(x) = (x^2 + 3x + 3x + 9) - 3x - 9
f(x) = x^2 + 6x + 9 - 3x - 9
f(x) = x^2 + 3x

f(x) = x^2 - 3x + 3