The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17 .
Explanation:
Here we have , [tex]g(x)=4x^2-16[/tex] 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 , [tex]g(x)=4x^2-16[/tex] . 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
⇒ [tex]g(x-9) = 4(x-9)^2-16[/tex]
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
Here , we g(x) is shifted by 9 units to the right so equation will be
⇒ [tex]g(x-9)-1 = (4(x-9)^2-16)-1[/tex]
g(x - 9) - 1 = 4(x - 9)² - 17.
Simplifying further
⇒ [tex]g(x-9)-1 = (4(x^2+81-18x)-17[/tex]
⇒ [tex]g(x-9)-1 = (4x^2+324-72x)-17[/tex]
⇒ [tex]g(x-9)-1 = 4x^2-72x+306[/tex]
Therefore , The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17.
