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So firstly, we have to figure out what the vertex is. The best method of doing this is by converting the standard form equation to vertex form.

First step is to separate x^2-4x and 12 with parentheses:

Next, to make what's inside the parentheses a perfect square, we want to find what is half of the x coefficient and then square that. In this case, that is four. Add 4 inside of the parentheses, and add -4 outside of the parentheses:

Next, you want to factor (x^2-4x+4), which is (x-2)^2, and combine 12 and -4 together, and your vertex form is

Now that we have the vertex form, we can find the vertex. To find this, if the vertex form was , then the vertex is (h,k). In this context, h = 2 and k = 8, therefore your vertex is (2,8) and the table with that vertex is the fourth table.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

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