Answer:
The missing value in last step is 3
Step-by-step explanation:
Given the function f(x)
[tex]f(x)=18x+3x^2[/tex]
Here some steps are given to write the above function in vertex form.
Step 1: Factor a out of the first two terms
[tex]f(x)=3(x^2+6x)[/tex]
Step 2: Form a perfect square trinomial.
[tex]f(x) = 3(x^2 + 6x + 9) - 3(9)[/tex]
Write the trinomial as a binomial squared.
By the identity of binomial square
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
[tex]x^2 + 6x + 9=x^2+2(x)(3)+3^2[/tex]
[tex]\text{Put a=x and b=3 in the identity, we get}[/tex]
[tex]x^2+2(x)(3)+3^2=(x+3)^2[/tex]
[tex]x^2 + 6x + 9=(x+3)^2[/tex]
Hence, the f(x) can be written as
[tex]f(x) = 3(x+3)^2 - 3(9)[/tex]
Therefore, the missing value in last step is 3
