To solve for [tex]\( f(0) \)[/tex] given the function [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex], we 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 terms inside the function:
[tex]\[
2(0)^2 = 0 \quad \text{and} \quad \sqrt{0 + 2} = \sqrt{2}
\][/tex]
3. Calculate the value of the square root:
[tex]\[
\sqrt{2} \approx 1.414213562
\][/tex]
4. Multiply by the coefficients:
[tex]\[
5 \times \sqrt{2} = 5 \times 1.414213562 \approx 7.07106781
\][/tex]
5. Add the calculated values:
[tex]\[
0 + 7.07106781 = 7.07106781
\][/tex]
6. Finally, round the result to the nearest hundredth:
[tex]\[
7.07106781 \approx 7.07
\][/tex]
Thus, the value of [tex]\( f(0) \)[/tex] rounded to the nearest hundredth is:
[tex]\[
f(0) \approx 7.07
\][/tex]
