What is the first step in writing [tex]f(x) = 6x^2 + 5 - 42x[/tex] in vertex form?

A. Factor 6 out of each term.
B. Factor 6 out of the first two terms.
C. Write the function in standard form.
D. Write the trinomial as a binomial squared.



Answer :

To transform the function [tex]\( f(x) = 6x^2 + 5 - 42x \)[/tex] into vertex form, we first need to rewrite it in a useful intermediate form. Here's how we can do it step-by-step:

1. Write the function in standard form:
The given function is already in standard form as [tex]\( f(x) = 6x^2 + 5 - 42x \)[/tex]. To better see the terms, we can reorganize it:
[tex]\[ f(x) = 6x^2 - 42x + 5 \][/tex]

2. Factor out the leading coefficient from the quadratic and linear terms:
The standard form of a quadratic function is [tex]\( ax^2 + bx + c \)[/tex], and here [tex]\( a = 6 \)[/tex], [tex]\( b = -42 \)[/tex], and [tex]\( c = 5 \)[/tex].

To complete the square, we start by factoring out the coefficient [tex]\( 6 \)[/tex] from the quadratic term and the linear term:
[tex]\[ f(x) = 6(x^2 - 7x) + 5 \][/tex]

Thus, the first step in writing [tex]\( f(x) = 6x^2 + 5 - 42x \)[/tex] in vertex form is to factor 6 out of the first two terms of the quadratic expression.