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?

how do I do this?

When x=3, one wants y to be 10
y= (x+a)^3 + 2
20= (3+a)^3 + 2

solve for a. I would change it to
18=(3+a)^3 and take the cube root of each side to solve for a.

I think we need to make it
10=(x+a)^3 + 2 or
8=(x+a)^3 so 8^(1/3)=x+a, then solve this when x=3
Then substitute that into y=(x+a)^3 + 2.

thanks for your help but I am still confused of how to find a right like i got up to here:8=(3+a)^3
then I have to cube it but how? like what would i end up with? I am a little confused!

Ok, here's what we know.
y=x^3 + 2
We first determine the value of x that corresponds to y=10, thus
10=x^3 + 2, which means 8=x^3 and x=2
We know that we want the value x=2 to now be shifted to the right to correspond to x=3. This means we need to subtact 1 from x in shifting to the right (it seems a little counter-intuitive, but study it a bit.)
Thus y=(x-1)^3+2 is the desired shift.
Substitute x=3 and we have y=(3-1)^3+2=2^3 + 2=10.
What would be the shift if we wanted the same graph to coincide with (3,2)?
How about (-4,10)?

Take the cube root of each side...

2= a+3 solve for a. My solution above is wrong, a typo.
repost if you have questions.

Oh dear, it seems like there was a lot of confusion in the previous responses. Let me try to clarify it for you.

To find the horizontal translation, you need to find the value of "a" that will shift the graph of y = x^3 + 2 so that it passes through the point (3, 10).

Here's what you need to do step by step:

1. Substitute the coordinates of the given point (x, y) = (3, 10) into the original equation: y = x^3 + 2.
This gives you 10 = 3^3 + 2.

2. Simplify the equation: 10 = 27 + 2.

3. Solve for the value of "a" by subtracting 2 from both sides: 10 - 2 = 27 + 2 - 2.
This gives you 8 = 27.

4. Oops, that's obviously not correct! There must have been an error in the calculations.

5. Let's retrace our steps. Starting from the given point (3, 10), we want to shift it horizontally to the right by a certain amount.

6. Since we're moving to the right, we subtract a value from "x" in the original equation. Let's call this value "a".

7. The new equation would be y = (x - a)^3 + 2.

8. Now we need to find the correct value of "a" that makes the new equation pass through the given point (3, 10).

9. Substitute the coordinates of the given point (x, y) = (3, 10) into the new equation: 10 = (3 - a)^3 + 2.

10. Simplify the equation: 10 = (3 - a)^3 + 2.

11. Solve for "a". You can do this by subtracting 2 from both sides, isolating the (3 - a)^3 term, and then taking the cube root of both sides.

12. Once you find the value of "a", substitute it back into the new equation y = (x - a)^3 + 2 to get the final equation.

I hope this clears things up for you! And remember, sometimes math can be confusing, but with a little perseverance, you'll clown your way to the right answer.

To find the correct value for a in the equation 8=(3+a)^3, you can take the cube root of each side.

Cube root of 8 is 2:

2 = 3 + a

Now, subtract 3 from both sides to isolate 'a':

2 - 3 = a

a = -1

So, the value of 'a' is -1.

To find the new equation, we substitute the value of 'a' into the equation y = (x + a)^3 + 2:

y = (x - 1)^3 + 2

Therefore, the new equation for the graph after applying a horizontal translation to pass through (3, 10) is y = (x - 1)^3 + 2.

To find the value of "a" in the equation y = (x + a)^3 + 2, where the graph passes through the point (3, 10), follow these steps:

1. Substitute the coordinates of the point (3, 10) into the equation:
10 = (3 + a)^3 + 2

2. Simplify the equation:
8 = (3 + a)^3

3. Take the cube root of both sides to solve for "a":
∛8 = ∛(3 + a)^3
2 = 3 + a

4. Solve for "a":
2 - 3 = a
a = -1

So the value of "a" is -1, which means the equation for the new graph after the horizontal translation is y = (x - 1)^3 + 2.

To verify, substitute x = 3 into the new equation:
y = (3 - 1)^3 + 2
y = 2^3 + 2
y = 8 + 2
y = 10, which is the same as the given point (3, 10).