Question

question 21 of 25 if $f(x)=x^2 + 3x + 5$, what is $f(a + h)$? a. $(x^2 + 3ax + 5)(a + h)$ b. $(a + h)^2 + 3(a + h) + 5(a + h)$ c. $h^2 + 3a + 3h + 5$ d. $a^2 + 2ah + h^2 + 3a + 3h + 5$

Explanation:

Step1: Substitute $x=a+h$ into $f(x)$

$f(a+h)=(a+h)^2 + 3(a+h) + 5$

Step2: Expand $(a+h)^2$ using formula

$(a+h)^2 = a^2 + 2ah + h^2$

Step3: Expand $3(a+h)$

$3(a+h)=3a+3h$

Step4: Combine all terms

$f(a+h)=a^2 + 2ah + h^2 + 3a + 3h + 5$

Answer:

D. $a^2 + 2ah + h^2 + 3a + 3h + 5$