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svp [43]
1 year ago
8

For the function defined by y = StartFraction 1 Over x squared EndFraction, if x is doubled, what is the effect on y?

Mathematics
1 answer:
olchik [2.2K]1 year ago
3 0

Answer:

a. y is quartered.

Step-by-step explanation:

y=1/x^2

when x is doubled, the equation becomes:

y=1/(2x)^2=1/(4x^2)

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This expression should do

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What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49
agasfer [191]

Answer:

The vertex is (3,4)

Step-by-step explanation:

To convert a quadratic from  

y = a x 2 + b x + c

form to vertex form,

y = a ( x − h ) 2 + k , you use the process of completing the square.

First, we must isolate the  x

terms:

y − 49 = 5 x 2 − 30 x + 49 − 49

y − 49 = 5 x 2 − 30 x

We need a leading coefficient of  1

for completing the square, so factor out the current leading coefficient of 2.

y − 49 = 5 ( x 2 − 6 x )

Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by  

2

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y − 49 + ( 5 ⋅ ? ) = 5 ( x 2 − 6 x + ? )

<- Hint:  

62 = 3 ;  3 ⋅ 3 = 9

y − 49 + ( 5 ⋅ 9 ) = 5 ( x 2 − 6 x + 9 )  

y− 49 + 45 = 5 ( x 2 − 6 x + 9 )

y − 4 = 5 ( x 2 − 6 x + 9 )

Then, we need to create the square on the right hand side of the equation:

y − 4 = 5 ( x − 3 ) 2

Now, isolate the  y  term:

y − 4 + 4 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

The vertex is:  

( 3 , 4 )

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</span>
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7 0
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