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skelet666 [1.2K]
3 years ago
10

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Mathematics
2 answers:
LekaFEV [45]3 years ago
5 0
For f(x) to be g(x), the equation f(x) would shift left one
swat323 years ago
4 0

Answer:

graph of g(x) will be translated 1 unit to the left

Step-by-step explanation:

g(x) = x^2 + 2x +1

LEts write the given g(x) in vertex form

WE apply completing the square method

WE take coefficient of x and then divide it by 2 and then square it

2 by 2= 1

1^2=1

add and subtract 1

g(x) = x^2 + 2x +1

g(x) =(x^2 + 2x +1)-1+1

now we factor  x^2+2x+1= (x+1)(x+1)

g(x) =(x+1)(x+1)-1+1

g(x) =(x+1)^2

Now we compare with the graph of f(x)= x^2

In g(x), 1 is added with x

So graph of g(x) will be translated 1 unit to the left

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Which expression is equivalent to the given expression?
PSYCHO15rus [73]

Answer:

-5(y - 3)(y - 7)

Step-by-step explanation:

Factor -5 out of all 3 terms:

-5(y^2 - 10y + 21)

Continue the factoring:

-5(y - 3)(y - 7)

Note:  when answer choices are given, kindly share them.  Thank you.

6 0
3 years ago
One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at a rate of 5/9 gallon per 2/3 hour. Which
anzhelika [568]
First recognize that the unit rate we're finding is gallons per hour, or \frac{g}{h}.

rate for Tank 1 = x gallons per hour = <em>a</em> gallons / <em>b</em> hours

T_{1}=\frac{\frac{5}{8}}{\frac{7}{10}}\\\\T_{1}=\frac{5}{8}*\frac{10}{7}\\\\T_{1}=\frac{50}{56}\\\\\\Fill\ rate\ of\ Tank\ 1=\frac{25}{28}


rate for Tank 2 = y gallons per hour = <em>c</em> gallons / <em>d</em> hours

T_{2}=\frac{\frac{5}{9}}{\frac{2}{3}}\\\\T_{2}=\frac{5}{9}*\frac{3}{2}\\\\T_{2}=\frac{15}{18}\\\\T_{2}=\frac{15}{18}\\\\\\Fill\ rate\ of\ Tank\ 2=\frac{5}{6}
3 0
3 years ago
6[ 5x (41-36) - (8+14)]
IgorLugansk [536]

Answer:

=18

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Subract (8x+6)-(x+4)
NeX [460]

Step-by-step explanation:

8x + 6) - (x + 4)

8x + 6 - (x + 4)

8x + 6 - x - 4

7x + 2

4 0
3 years ago
Calvin is painting an area that is 115 square feet. He is able to paint 2.5 square feet every 2 minutes. At this rate , how long
Verdich [7]

Answer:

Calvin will paint the entire area in 92 minutes or 1 hour 32 minutes.

Step-by-step explanation:

First of all we know that the total surface are that Calvin is painting is 115 square feet.

The rate at which Calvin is painting refers to the surface area he covers every 2 minutes. This is 2.5 square feet every 2 minutes.

we can set up a relation to solve this problem

If Calvin paints 2.5 ft^{2} in 2 minutes

He will paint 115 ft^{2} in x minutes

By cross multiplying, we have x= \frac{2 \times 115}{2.5}=92 minutes

Hence Calvin will paint the entire area in 92 minutes or 1 hour 32 minutes.

3 0
3 years ago
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