Answer :
Let's find [tex]\(f(0)\)[/tex] for the function [tex]\(f(x) = 2(x)^2 + 5 \sqrt{(x+2)}\)[/tex].
1. Firstly, substitute [tex]\(x = 0\)[/tex] into the function:
[tex]\[ f(0) = 2(0)^2 + 5 \sqrt{(0 + 2)} \][/tex]
2. Simplify the expression:
[tex]\[ f(0) = 2 \cdot 0^2 + 5 \sqrt{2} \][/tex]
3. Recognize that [tex]\(0^2\)[/tex] is 0:
[tex]\[ 2 \cdot 0^2 = 0 \][/tex]
and thus:
[tex]\[ f(0) = 0 + 5 \sqrt{2} \][/tex]
4. Finally, calculate [tex]\(5 \sqrt{2}\)[/tex]. The value of [tex]\(\sqrt{2}\)[/tex] is approximately 1.414. Therefore:
[tex]\[ 5 \sqrt{2} \approx 5 \times 1.414 = 7.07 \][/tex]
So, [tex]\(f(0) = 7.07\)[/tex] when rounded to the nearest hundredth.
Therefore, the completed statement is:
[tex]\[ f(0) = 7.07 \][/tex]
1. Firstly, substitute [tex]\(x = 0\)[/tex] into the function:
[tex]\[ f(0) = 2(0)^2 + 5 \sqrt{(0 + 2)} \][/tex]
2. Simplify the expression:
[tex]\[ f(0) = 2 \cdot 0^2 + 5 \sqrt{2} \][/tex]
3. Recognize that [tex]\(0^2\)[/tex] is 0:
[tex]\[ 2 \cdot 0^2 = 0 \][/tex]
and thus:
[tex]\[ f(0) = 0 + 5 \sqrt{2} \][/tex]
4. Finally, calculate [tex]\(5 \sqrt{2}\)[/tex]. The value of [tex]\(\sqrt{2}\)[/tex] is approximately 1.414. Therefore:
[tex]\[ 5 \sqrt{2} \approx 5 \times 1.414 = 7.07 \][/tex]
So, [tex]\(f(0) = 7.07\)[/tex] when rounded to the nearest hundredth.
Therefore, the completed statement is:
[tex]\[ f(0) = 7.07 \][/tex]
