Question

deling and analyzing quadratic functions: quadratic functions the steps in writing $f(x) = 18x + 3x^2$ form are shown, but a value is missing in the last step. write the function in standard form. $f(x) = 3x^2 + 18x$ factor $a$ out of the first two terms. $f(x) = 3(x^2 + 6x)$ form a perfect square trinomial. $left(\frac{6}{2}\
ight)^2 = 9$ $f(x) = 3(x^2 + 6x + 9) - 3(9)$ write the trinomial as a binomial squared. $f(x) = 3(x + \\_\\_\\_\\_)^2 - 27$ what is the missing value in the last step? 18 6 9 3

Explanation:

Step1: Recall perfect square trinomial rule

A perfect square trinomial $x^2 + bx + c$ follows $(x+\frac{b}{2})^2 = x^2 + bx + (\frac{b}{2})^2$.

Step2: Identify $b$ in the trinomial

In $x^2+6x+9$, $b=6$. Calculate $\frac{b}{2}=\frac{6}{2}=3$.

Step3: Verify the binomial square

$(x+3)^2 = x^2 + 6x + 9$, which matches the trinomial inside the parentheses.

Answer:

3