To solve the problem where we need to find the value of the function [tex]\( f(x) = 2(x)^2 + 5 \sqrt{(x+2)} \)[/tex] when [tex]\( x = 0 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 2(0)^2 + 5 \sqrt{(0+2)}
\][/tex]
2. Simplify the expression:
- First, calculate [tex]\( 2(0)^2 \)[/tex]:
[tex]\[
2(0)^2 = 2 \cdot 0^2 = 2 \cdot 0 = 0
\][/tex]
- Next, calculate [tex]\( 5 \sqrt{(0+2)} \)[/tex]:
[tex]\[
\sqrt{(0+2)} = \sqrt{2}
\][/tex]
[tex]\[
5 \sqrt{2}
\][/tex]
3. Combine the results:
[tex]\[
f(0) = 0 + 5 \sqrt{2}
\][/tex]
4. Calculate the value of [tex]\( 5 \sqrt{2} \)[/tex]:
The value of [tex]\( \sqrt{2} \approx 1.414213562 \)[/tex]. Therefore,
[tex]\[
5 \sqrt{2} \approx 5 \cdot 1.414213562 = 7.0710678118654755
\][/tex]
5. Round the result to the nearest hundredth:
[tex]\[
7.0710678118654755 \approx 7.07
\][/tex]
Thus, the value of [tex]\( f(0) \)[/tex] is:
[tex]\[
f(0) = 7.07
\][/tex]
