Find the values of a and b such that x^2-4x+9=(x+a)^2+b
1 answer:
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Answer: (4, 4.6)
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The x coordinates of the points (3,2) and (8,15) are x = 3 and x = 8 respectively. The distance between these x values is 8-3 = 5 units. So we move 5 units to the right to go from the first point to the second point.
Imagine we had 5 blocks. If 1 of them is colored red and the other four are green, then the ratio of red to green is 1:4. We have 1 part red, 4 parts green. So 1+4 = 5 total. The "red block" in the metaphor mentioned basically tells us how far to move over the total distance 5. So we move 1/5th of the way along the horizontal distance of 5.
1/5 of 5 = (1/5)*5 = 1
So we move exactly one unit along the x direction. Therefore, we add 1 to to the x coordinate of (3,2) to end up with (3+1,2) = (4,2). This isn't the final answer, but it helps get us closer.
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For the y coordinates of the given points we see that the y difference is 15-2 = 13. Multiply this by 1/5 to get
(1/5)*13 = 13/5 = 2.6
We follow effectively the same steps as before, but now we're dealing with the y values this time. So we move 2.6 units in the y direction (ie move 2.6 units up)
Add 2.6 onto the y value of that last point we found to get (4,2+2.6) = (4,4.6)
So that explains why the answer is (4, 4.6)
A visual might help so I've posted one below in the attached images. In that image, the location of point T is the final answer.
