Question

Which of the following equations represents the pattern above?
A. y = (2x + 4)2


B. y = (2x + 1)2 + 4


C. y = (2x)2 + 4


D. y = (2x - 1)2 + 4

Answer 1

Easy to see the pattern once you temporarily eliminate the cross "tips" (4 squares in each diagram) and add them back at the end. Hint: without the cross "tips", you get 1^2, 3^2, 5^2, ...

Answer 2

im not understanding

Answer 3

Taking the tips off, the diagrams look like:

Answer 4

That pattern is as I stated already. Then just add the tips back, which means adding 4 to each term in the sequence since EACH figure has the addition of 4 "tips" to the diagrams I drew.

Answer 5

In other words, with the "tips" (the original diagram), you see (1^2) + 4, (3^2) + 4, (5^2) + 4, etc. That's the pattern. The equation should be easy to spot from that.

Answer 6

The problem boils down to finding the pattern in the expression in the parentheses. In other words, what is the base of what is having an exponent attached to it. In simplest terms, the underlying pattern is in going from 1 to 3 to 5 to 7 to 9 to ...

Answer 7

still drawing a blank im sorri

Answer 8

In going from 1 to 3 to 5 to 7, we are progressing by "2" at a time, suggesting a factor of 2x. If we start with x = 0, we see 2x + 1 as fitting the pattern (within the parentheses). As x goes from 0 to 1 to 2 to 3 ..., we see 2x + 1 going from 1 to 3 to 5 to 7 .... Then square this. Then add 4.

Answer 9

is it B?

Answer 10

It actually could be either B or D, depending on whether you start with x = 0 or x = 1. They really are both true answers. But given that this is a multiple choice question, and keeping in mind that 1,2,3,4 is a more readily "logical" counting sequence (because those are natural numbers), I would pick D. Whoever set up the problem selection did a bad job of it.

Answer 11

The more I think about it, I am further convinced that the answer is D because the diagram is assigning a value of x to each particular figure and the counting mirrors going from counting the figures as figure1, figure2, figure3, etc. So, the answer is definitely D.

Answer 12

"D" is the correct answer. "B" would have been correct if the diagram labeled the figures as figure0, figure1, figure2, etc.

Answer 13

Is this making sense now?

Answer 14

yes thank you im sorri i was putting my son to bed but thank you so much for all of your help! u seem to be the only one who ever helps me