According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,463 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 49 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,640 square feet with a sample standard deviation of 66 square feet. Calculate the value of the test statistic.

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

12

step-by-step explanation:

the first option is the answer.