Question

what is the first step in writing f(x)=6x^2+5-42x 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 1

Answer:

Answer c): write the function in standard form

Step-by-step explanation:

To start with, it is important to write the polynomial in standard form, so as to have the two terms with the dependence in x together:

$6x^2-42\,x+5$

then you extract 6 as a common factor of just the terms with the variable x:

$6(x^2-7x)+5$

Then proceed to complete the square in the expression inside the parenthesis:

$6(x^2-7x+\frac{49}{4} -\frac{49}{4})+5$

$6\,((x-\frac{7}{2} )^2-\frac{49}{4} )+5\\6\,(x-\frac{7}{2} )^2-\frac{147}{2}+5\\6\,(x-\frac{7}{2} )^2-\frac{137}{2}$

Then, the function can be finally be written as:

$f(x)=6\,(x-\frac{7}{2} )^2-\frac{137}{2}$

in vertex form