Question

given the function, answer the following questions.\\( f(x) = -(x - 5)^2 + 16 \\)\
what are the solutions to \\( x \\)?\\( x = \\)\
what are the coordinate point(s) of the \\( x \\)-intercept(s)?\
if there are no \\( x \\)-intercepts, put dne in the answer box. do not use decimals.\
question help: \\( \boxed{\text{video}} \\)

Explanation:

Step1: Find x when f(x)=0

To find the x - intercepts, we set \(y = f(x)=0\). So we have the equation \(0=-(x - 5)^{2}+16\).
First, we can rewrite this equation as \((x - 5)^{2}=16\).

Step2: Solve for x

Taking the square root of both sides of the equation \((x - 5)^{2}=16\), we get \(x - 5=\pm\sqrt{16}=\pm4\).

• Case 1: When \(x - 5 = 4\), then \(x=4 + 5=9\).
• Case 2: When \(x - 5=-4\), then \(x=-4 + 5 = 1\).

Step3: Find the coordinate points

The x - intercepts occur where \(y = 0\). So the coordinate points of the x - intercepts are \((1,0)\) and \((9,0)\).

Answer:

The solutions for \(x\) are \(x = 1\) and \(x=9\). The coordinate points of the x - intercepts are \((1,0)\) and \((9,0)\).