Answer: [tex]g(x) = (x+3)^2 + 5[/tex]
Step-by-step explanation:
Here, the given function,
[tex]f(x) = x^2[/tex]
Which is the equation of parabola, having vertex (0,0)
When the function f(x) is transformed to a new function,
Then we can write the new equation of parabola,
[tex]g(x) = a(x-h)^2+k^2[/tex]
Where h shows the horizontal shifting and k shows the vertical shifting
While a shows the compression,
Here compression is not occur.
Therefore, a = 1
Now, f(x) is shifted three unit to the left
Therefore, h = - 3 ( In left side we take negative shifting)
Again, f(x) is shifted five unit up,
k = 5
(Note: In case of downward shifting the value of k will be negative)
By putting the values of a, h and k in the above transformed equation,
We get, [tex]g(x) = (x+3)^2 + 5[/tex]
Which is the required transformed equation.
⇒ Third Option is correct.
