Question

Please help meeee what is the answerrrr i need it asapp

Answer 1

The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17 .

Explanation:

Here we have , $g(x)=4x^2-16$ 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 , $g(x)=4x^2-16$ . 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

⇒ $g(x-9) = 4(x-9)^2-16$

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

⇒ $g(x-9)-1 = (4(x-9)^2-16)-1$

g(x - 9) - 1 = 4(x - 9)² - 17.

Simplifying further

⇒ $g(x-9)-1 = (4(x^2+81-18x)-17$

⇒ $g(x-9)-1 = (4x^2+324-72x)-17$

⇒ $g(x-9)-1 = 4x^2-72x+306$

Therefore , The new equation will be h (x) = g(x - 9) - 1 = 4(x - 9)² - 17.