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Fittoniya [83]
3 years ago
5

If you shift the quadratic parent function, f(x)=x2 , right 10 units, what is the equation of the new function?

Mathematics
1 answer:
tiny-mole [99]3 years ago
8 0

Answer:

Step-by-step explanation:

The standard form of a quadratic is

y=a(x-h)^2+k where h is side to side movement (it's also the x coordinate of the vertex) and k is the up or down movement (it's also the y coordinate of the vertex). If there is no up or down movement, the k value is 0. (We don't need to worry about the value for a here; it's 1 but that doesn't change anything for us in our problem). Movement to the right is positive, so we are moving +10. Filling that into our equation:

y=(x-(+10))^2 and simplified:

y=(x-10)^2  That is the parent graph shifted 10 units to the right.

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The given function is

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and the alternate triangle inequality property;

|x - y|  \geqslant  |x|  -  |y|

We apply this property to get:

y  \geqslant   |x |    - |3|    +  |x |  +  |2|  -(  |x |  -  |5| )

Expand parenthesis to get:

y  \geqslant   |x |    - |3|    +  |x |  +  |2|  - |x |   +   |5|

Simplify to get:

y  \geqslant   |x |    - 3+  |x |  +  2- |x |   +   5

Group similar terms to get:

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y  \geqslant   |5 |   + 4

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