The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17 .
<u>Explanation:</u>
Here we have , were shifted 9 units to the right 1 down , We need to find what would be the new equation . Let's find out:
Given equation is , . Let's have transformations as
- Shift by 9 units to the right
Here , we g(x) is shifted by 9 units to the right so equation will be
⇒
transformation rules
f(x)---> f(x-a)= Graph shifted to right by a units
f(x)---> f(x+a)= Graph shifted to left by a units
f(x)---> f(x)+a= Graph shifted upwards by a units
f(x)---> f(x)-a= Graph shifted downwards by a units
- Shift by 1 units to down
Here , we g(x) is shifted by 9 units to the right so equation will be
⇒
g(x - 9) - 1 = 4(x - 9)² - 17.
Simplifying further
⇒
⇒
⇒
Therefore , The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17.