Please help! A rectangular tabletop has an area of.


What are the possible dimensions of the tabletop? Use factoring.

The order doesn't matter, so you could say "t+11 and t-9" to mean the same thing.

Explanation:

Think of two numbers that multiply to -99, but also add to 2. In other words, find two factors of -99 which add to 2. We'll use trial and error.

Here are all the ways to multiply to -99 using integers only:

Add up each factor pair to see which sum is equal to 2.

We can see that 11 and -9 are the two numbers we're after, so therefore, t^2+2t-99 factors to (t-9)(t+11). The order doesn't matter with the factor multiplication.

As a more efficient alternative method, you can use the quadratic formula to solve t^2+2t-99 = 0 to end up with t = 9 and t = -11. That would lead to the  two equations t-9 = 0 and t+11 = 0. Applying the zero product property then gets us (t-9)(t+11) = 0.

To help show that (t-9)(t+11) becomes t^2+2t-99, you can use the FOIL rule to expand that factorization out. This is one way to verify the answer.

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