Questions: What are the (y)-intercepts ( f(x)=frac19(x-9)^2+9 )

$What are the (y)-intercepts ( f(x)=frac19(x-9)^2+9 )$

Transcript text: What are the $y$-intercepts \[ f(x)=\frac{1}{9}(x-9)^{2}+9 \]

Solution

To find the y-intercept of a function, we need to evaluate the function at $ x = 0 $.

Solution Approach

Step 1: Evaluate the Function at $ x = 0 $

To find the y-intercept of the function $ f(x) = \frac{1}{9}(x-9)^{2}+9 $, we substitute $ x = 0 $: \[ f(0) = \frac{1}{9}(0-9)^{2}+9 \]

Step 2: Simplify the Expression

Calculating $ (0-9)^{2} $: \[ (0-9)^{2} = 81 \] Now substituting back into the function: \[ f(0) = \frac{1}{9} \cdot 81 + 9 \]

Step 3: Calculate the Result

Calculating $ \frac{1}{9} \cdot 81 $: \[ \frac{1}{9} \cdot 81 = 9 \] Now adding $ 9 $: \[ f(0) = 9 + 9 = 18 \]

The y-intercept of the function is \$\boxed{18}\$.

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