Tabitha is raising money for the American Cancer Society. To raise money, she takes donations from family and friends and does a “walk-a-thon” where she will earn money for each mile she walks. She collects $18 for every mile that she walked. In addition, her grandmother gave her a $72 donation. She collected $234 in total.

Write and solve an equation to find the number of miles, m, Tabitha walked. Explain your equation in the context of this equation and validate your result.

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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