# Can You Solve for Y Using the Quadratic Formula?

• 1MileCrash
In summary, the conversation is discussing using the quadratic formula to find the solutions for the equation x=-6y^2 + 4y, and then plotting the resulting functions to create perpendicular parabolas. The speaker also mentions using completing the square as an alternative method.
1MileCrash
x=-6y^2 + 4y

Try completing the square (i.e. as-if it was just a normal quadratic equation of a single variable)... it should work.

okay, so plotting BOTH of these graphs will give me a perpendicular graph of y=-6x^2+4x, correct? each of the functions from the quadratic formula should be each half of a perpendicular parabola.

hhhmmm...I just took the equation and put it like this:

-6y2 + 4y - x = 0

and solved it using the quadratic formula, so

y = ( -b + sqrt(b2 - 4ac) ) / 2a

where

a=-6
b=4
c= -x

and the other solution to y is with the negative value of the square root.

I get something like this:

y = 1/3 + sqrt( (2-3x)/18 )

and, of course,

y = 1/3 - sqrt( (2-3x)/18 )

which tells me that x cannot be larger than 2/3, otherwise the radical becomes negative.

So, you can plot y versus x for -inf <= x <= 2/3

## 1. How do you solve for y?

To solve for y, you need to isolate it on one side of the equation. This can be done by using inverse operations, such as addition, subtraction, multiplication, and division. Once y is isolated, you can then solve for it by performing the operations on the other side of the equation.

## 2. What are the steps to solving for y?

The steps to solving for y may vary depending on the specific equation, but generally, the steps are as follows:

1. Identify the variable that you want to solve for (in this case, y).
2. Isolate the variable on one side of the equation by using inverse operations.
3. Perform the same operations on the other side of the equation.
4. If necessary, simplify the equation by combining like terms.
5. The remaining value next to the variable is the solution for y.

## 3. Can you provide an example of solving for y?

Sure, let's say we have the equation 3y + 6 = 18. To solve for y, we need to isolate it on one side of the equation. To do this, we can subtract 6 from both sides of the equation, giving us 3y = 12. Then, we divide both sides by 3, giving us y = 4. So the solution for y in this equation is 4.

## 4. What if there are variables on both sides of the equation?

If there are variables on both sides of the equation, the first step is to try to simplify the equation by combining like terms. Then, you can follow the same steps as mentioned earlier, isolating the variable you want to solve for and performing inverse operations on both sides of the equation.

## 5. Can you solve for y in any type of equation?

Yes, as long as there is a variable for y in the equation, it can be solved for. However, some equations may require more complex methods or multiple steps to solve for y.

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