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What is the first step in writing [tex]$f(x) = 3x^2 + 6x - 8$[/tex] in vertex form?

A. Factor out 3 from each term.
B. Form a perfect square trinomial by keeping the value of the function equivalent.
C. Write the trinomial as a binomial squared.
D. Factor out 3 from the first two terms.

Sagot :

GinnyAnswer
To begin the process of converting the quadratic function [tex]\( f(x) = 3x^2 + 6x - 8 \)[/tex] into vertex form, the first step is:

Factor out 3 from the first two terms.

Here's how you can do it step-by-step:

1. Factor out 3 from the first two terms:

The quadratic term [tex]\( 3x^2 \)[/tex] and the linear term [tex]\( 6x \)[/tex] share a common factor of 3. So, you can factor 3 out from these two terms.

[tex]\[ f(x) = 3(x^2 + 2x) - 8 \][/tex]

This step sets up the expression to more easily complete the square in the next steps, ultimately converting it into vertex form [tex]\( a(x - h)^2 + k \)[/tex].
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