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kemzzoo7206
01.04.2021 •
Mathematics
Please help! quadratic formulas
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Ответ:
A.
See Explanation
B.
Vertical shift:![k = 8](/tpl/images/0979/5534/2ece0.png)
Horizontal shift:![k = 16](/tpl/images/0979/5534/68f85.png)
C.
The horizontal shift is:![f(x + k) = g(x)](/tpl/images/0979/5534/238e8.png)
The vertical shift is:![f(x) = g(x) - k](/tpl/images/0979/5534/bbc37.png)
Step-by-step explanation:
See attachment for graph
A. The possible transformation from f(x) to g(x)
From the attachment, g(x) can be translated or shifted to f(x) in two possible ways.
1. Horizontal Shift which shifts g(x) by k units to the right
And
2. Vertical Shift which shifts g(x) downwards by k units
B. Solve for k
First, we calculate the equations of both lines.
However, we need to calculate the slope (m) of both to do so:
For f(x)
So:
The equation is then:
Where:
So:
For g(x)
So:
The equation is then:
Where:
So:
So, we have:
For the horizontal shift:
--------------------------------------------------------------------------------------------------------------
If
then
--------------------------------------------------------------------------------------------------------------
So, we have:
Subtract 2x from both sides
Add 10 to both sides
Divide through by 2
For the horizontal shift:
Subtract 2x from both sides
Subtract 6 from both sides
Multiply both sides by -1