Please help me find x of: x-5=11-3
2 answers:
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<h3>Answer:</h3>
- g(x) has an axis of symmetry at x = 3
- g(x) is shifted right 3 units from the graph of f(x)
- g(x) is shifted up 4 units from the graph of f(x)
The vertex form of g(x) is ...
... g(x) = -(x -3)² +4
This is offset to the right by 3 and up by 4 from the parent function. (It is also first reflected across the x-axis.)
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<em>Vertex form</em>
You know the leading coefficient is -1 because that's what it is for x² in the given form. When you factor -1 from the first two terms, of the given form, you have ...
... g(x) = -1(x² -6x) -5
Half the x coefficient inside parentheses will be the constant in the squared binomial term, so that term is (x -3)². The constant in that square is +9, so adding that value inside and outside parentheses in g(x) gives ...
... g(x) = -1(x² -6x +9) -5 +9
... g(x) = -(x -3)² +4 . . . . . vertex form
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<em>About transformations</em>
g(x) = f(x -a) causes the graph of f(x) to be shifted "a" units to the right. For a function f(x) with an axis of symmetry at x=0, it moves the axis of symmetry to x=a.
g(x) = f(x) +a causes the graph of f(x) to be shifted "a" units up.
g(x) = -f(x) causes the graph of f(x) to be reflected across the x-axis.
Here, we have all three of these transformations. First is the reflection:
... f₁(x) = -f(x) = -x²
Then we have shifting to the right 3 units. (also moves the axis of symmetry)
... f₂(x) = f₁(x-3) = -(x -3)²
Finally, we have shifting up 4 units.
... g(x) = f₂(x) +4 = -(x -3)² +4
<u>Complete Question:</u>
Corinne is taking a train into the city. The train travels at a rate of 45 miles per hour. Which quantity depends on the other?
A. The distance traveled depends on the number of hours traveled.
B. The number of hours traveled depends on the speed of the train.
C. The speed of the train depends on the distance traveled.
D. The speed of the train depends on the number of hours traveled.
<u>Answer:</u>
Corinne is taking a train into the city. The train travels at a rate of 45 miles per hour. The distance traveled depends on the number of hours traveled
<u>Step-by-step explanation:</u>
As we know the velocity can de defined as the rate of change of position of objects in a particular time. The formula is given by,
Here, in the question, rate of speed of train is given as 45 miles per hour. if we keep the velocity as constant one, then distance is directly proportionate to the travelled time
If 'v' is constant,
By this we can conclude that, the distance travelled by the train depends on the time taken to travel to it. Hence option A would be the correct one.