Please answer if you know
5y^2 - 2 = 3y

y= -2/5 and y=1

Step-by-step explanation:

Start by transforming the equation to your liking:

Now we have to factor! To do this we have to find common numbers. Do this by multiplying -2 and 5 to get -10. Now think about which two numbers add multiply to be -10 but also add up to be -3 (I got this number from the middle of the equation). The two numbers you should've got are -5 and 2.

Now substitute those two number in place of the middle term, which is -3y like so:

Now solve the equation in pieces... find the greatest common factor from and the greatest common factor from . The two common factors for both of those are 5y and 2. Your equation should now look like this:

+

The two greatest common factors become into one group and the other equation that they have in common (y-1) is it's own equation:

Now equal both of the equations to 0 and solve for y to get both of the values of y.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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