The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours: A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Island in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 31, 62, 93, 124, 155, 186, 217, 248, 279. The graph shows a straight line joining the ordered pairs 0, 31, and 1, 93, and 2, 155, and 3, 217, and 4, 279.

What is the speed of the motorboat?

62 miles per hour
93 miles per hour
31 miles per hour
279 miles per hour

a

explanation:

ab will be equal to

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

i believe so, according to my "strange" way of figuring out weird math problems like this.