SOLUTION: In a quadratic equations why does the y value for subsequent x values increase or decrease in a pattern. For example, in the equation x^2 -2x -3, the y value when x is 1(vertex), 2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: In a quadratic equations why does the y value for subsequent x values increase or decrease in a pattern. For example, in the equation x^2 -2x -3, the y value when x is 1(vertex), 2      Log On


   

Question 637355: In a quadratic equations why does the y value for subsequent x values increase or decrease in a pattern. For example, in the equation x^2 -2x -3, the y value when x is 1(vertex), 2, 3, and 4 is -4(vertex), -3, 0, and 5 respectively. Every time the y value is increasing by 1, then 3, then 5, then 7, then 9, and so on. Please explain this!
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a quadratic equations why does the y value for subsequent x values increase or decrease in a pattern. For example, in the equation x^2 -2x -3, the y value when x is 1(vertex), 2, 3, and 4 is -4(vertex), -3, 0, and 5 respectively. Every time the y value is increasing by 1, then 3, then 5, then 7, then 9, and so on. Please explain this!
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The axis of symmetry is a vertical line through the vertex at x = 1.
The curve is symmetric (left to right) on x = 1.
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Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

y = x^2 -2x -3       | y = ax^2 + bx + c  and -b%2F2a+=+2%2F%282%2A2%29+=+highlight%281%29

y =+%28x-highlight%281%29%29%5E2+-+1+-+3+   |completing the Square to find Vertex form

y = (x-1)^2 - 4 ,    V%281%2C-4%29

y=a%28x-h%29%5E2+%2Bk, the vertex form of a parabola,  where(h,k) is the vertex

The pattern You are seeing is the result of the (x-1)^2 pattern

x   (x-1)^2	y

1	0	-4

2	1	-3

3	4	0

4	9	5

5	16	12