Dukell24idn
Answered

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Complete the statements below to show [tex][tex]$y=x^2+2x-1$[/tex][/tex] being converted to vertex form.

Form a perfect-square trinomial.
[tex]
y = x^2 + 2x + \square - 1 - \square
[/tex]

Sagot :

GinnyAnsweridn
To convert the quadratic equation [tex]\( y = x^2 + 2x - 1 \)[/tex] to vertex form by completing the square, we follow these steps:

We start with:
[tex]\[ y = x^2 + 2x - 1 \][/tex]

Step 1: Form a perfect-square trinomial

We focus on the quadratic and linear terms: [tex]\( x^2 + 2x \)[/tex].

To form a perfect-square trinomial, we add and subtract the square of half the coefficient of [tex]\( x \)[/tex].

The coefficient of [tex]\( x \)[/tex] is 2. Half of 2 is 1, and [tex]\( 1^2 = 1 \)[/tex].

So, we add and subtract 1 inside the equation:

[tex]\[ y = x^2 + 2x + 1 - 1 - 1 \][/tex]

Therefore, the equation becomes:
[tex]\[ y = x^2 + 2x + 1 - 1 - 1 \][/tex]

So, the answer to filling in the blanks is:
[tex]\[ y = x^2 + 2x + \boxed{1} - 1 - \boxed{1} \][/tex]
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