QUESTION: A horizontal translation is applied to the graph of y= X^ 3 + 2 so that it will pass through (3, 10) what is the new equation for the graph?
y=(x+a) ^3+ 2
10= (3+ a) ^3 + 2
10-2= (3+ a) ^3 + 2-2
8= (3+ a) ^3
Take the cube root of each side...
2= 3-a solve for a
So I went like this:
2-2+a= 3-a-2+a
a= 1
So the new equation would be? I am unsure which equation do I put it in for?
8= (3+ a) ^3
Take the cube root of each side...
2= 3-a solve for a ****Nope, you changed the sign on a. 1=3+a, a=-1
The new equation is
y=(x-1)^3 +2 This shifts the equation along the horizontal axis to the right.
To find the new equation for the graph, you correctly started with the equation y = (x + a)^3 + 2, where "a" represents the horizontal translation. Then, you substituted the coordinates (3, 10) into the equation to find the value of "a".
However, there was a mistake in your calculations. When you simplified 10 - 2 and 2 - 2, you correctly obtained 8 = (3 + a)^3, but when you took the cube root of both sides, you wrote 2 = 3 - a. Instead, taking the cube root of 8 gives you 2 = 3 + a.
To solve for "a", you need to isolate "a" on one side of the equation. So, subtracting 3 from both sides, you get 2 - 3 = a, which simplifies to a = -1.
Therefore, the correct value for "a" is -1. Substituting this value back into the equation y = (x + a)^3 + 2, you get y = (x - 1)^3 + 2. This is the new equation for the graph, which represents a horizontal shift to the right by one unit.