Question

given the function, answer the following questions below.\\( f(x) = -(x - 5)^2 + 16 \\)\
what are the solutions to \\( x \\)?\\( x = \\)\
question help: \\( \triangledown \\) video

Explanation:

Step1: Set the function to zero

To find the solutions for \( x \) when \( f(x) = 0 \), we start with the equation \( -(x - 5)^2+ 16=0 \).

Step2: Rearrange the equation

First, we can rewrite the equation as \( (x - 5)^2=16 \).

Step3: Take square roots

Taking the square root of both sides, we get \( x - 5=\pm\sqrt{16} \). Since \( \sqrt{16} = 4 \), this becomes \( x - 5=\pm4 \).

Step4: Solve for \( x \)

For the case \( x - 5 = 4 \), we add 5 to both sides: \( x=4 + 5=9 \).
For the case \( x - 5=- 4 \), we add 5 to both sides: \( x=-4 + 5 = 1 \).

Answer:

The solutions for \( x \) are \( 1 \) and \( 9 \), so \( x = 1,9 \)