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What is the first step when rewriting [tex]$y = 3x^2 + 9x - 18$[/tex] in the form [tex]$y = a(x-h)^2 + k$[/tex]?

A. 3 must be factored from [tex][tex]$3x^2 + 9x$[/tex][/tex].
B. [tex]$x$[/tex] must be factored from [tex]$3x^2 + 9x$[/tex].
C. 9 must be factored from [tex][tex]$9x - 18$[/tex][/tex].
D. 3 must be factored from [tex]$3x^2 - 18$[/tex].


Sagot :

To begin rewriting the quadratic equation [tex]\( y = 3x^2 + 9x - 18 \)[/tex] in the form [tex]\( y = a(x - h)^2 + k \)[/tex], which is known as vertex form, the first step is to factor 3 from the terms involving [tex]\( x \)[/tex], namely [tex]\( 3x^2 + 9x \)[/tex].

Here is a detailed, step-by-step solution:

1. Start with the original equation:
[tex]\[ y = 3x^2 + 9x - 18 \][/tex]

2. Factor out 3 from the terms [tex]\( 3x^2 \)[/tex] and [tex]\( 9x \)[/tex]:
[tex]\[ y = 3(x^2 + 3x) - 18 \][/tex]

Therefore, the first step is to factor 3 from the expression [tex]\( 3x^2 + 9x \)[/tex], and you end up with:
[tex]\[ 3(x^2 + 3x) - 18 \][/tex]

Hence, the correct step is: [tex]\( \boxed{3 \text{ must be factored from } 3x^2 + 9x} \)[/tex].