The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
<h3>
How does the graph of g(x) compare to the one of f(x)?</h3>
Here we have:
You can notice that if we take f(x), and we shift it 2 units to the right, we have:
g(x) = f(x - 2)
Then if we apply a shift upwards of 6 units, then we have:
g(x) = f(x - 2) + 3
Replacing f(x) by the cubic parent function, we have:
So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
If you want to learn more about translations:
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Answer:
Step-by-step explanation:
We need to write a quadratic equation so we can use standard quadratic equation:
Plug the given points to get three equations.
for (7,4), we plug x=7 and y=4
...(i)
similarly using other two points, we get:
...(ii)
...(iii)
Now we solve those three equations by any method like substitution, or matrices or by any method and get:
Now plug these values into , we get final equation as:
Answer:
By adding 4 to both sides.
2= -4 +b
2= b -4
2+4= b-4 +4
6= b
Another way to look at it is to move all the constants to one side. Here we have the constant 2 on the left hand side, and on the right we have the constant -4 and the variable b.
To isolate b, we move the constant -4 to the left hand side. Moving a number to the other side of the equal sign changes the sign of the number. So, -4 becomes a +4 on the left hand side.
2 +4= b
6= b
3/4 equals 15/20, so b+3=15. B=12
