The curve y=x^3 is translated by p units, parallel to the x axis. State the equation of the curve after it has

Question

The curve y=x^3 is translated by p units, parallel to the x axis. State the equation of the curve after it has been transformed


Please help! Thanks alot!

Answer 1

The curve y=x³ is translated by p units, parallel to the x axis. State the equation of the curve after it has been transformed

y = (x - p)³ (given that p > 0 in the positive x direction and p < 0 in the negative x direction)

Answer 2

y = x^2 + 7x + 3. At P, x = 0, so y = 3, and P is (0,3) dy/dx = 2x + 7. whilst x = 0, dy/dx = 7, so the gradient of the tangent to the curve at (0,3) is 7, so the equation of the tangent to the curve is y = 7x + c whilst x = 0, y = 3, so 3 = 0 + c, so c = 3, and the equation of the tangent to the curve at P is: y = 7x + 3.

Answer 3

You're shifting the whole thing up or down the y axis by p units so it's
y = x^3 + p

Answer 4

before the translation,
the equation is

y=x^3

after the translation,
if the graph shifted p
units in the x +ve
direction,the equation is

y=(x-p)^3

after the translation,
if the graph shifted p
units in the x -ve
direction,the equation is

y=(x+p)^3

{note:if you want to shift
the graph p units in the y +ve
direction,the equation is
y=x^3+p
if you want to shift
the graph p units in the y -ve
direction,the equation is
y=x^3-p}

i hope that this helps

Answer 5

Before translation: y = x^3
After translation: y = (x - p)^3

Answer 6

y=(x-p)^3

Answer 7

transformed how? its already parrallel to the x-axis so what type of movement is there?

Answer 8

stop cheating!!!