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The vertex form of the equation of a parabola is [tex]\( y = (x-3)^2 + 36 \)[/tex]. What is the standard form of the equation?

A. [tex]\( y = x^2 + 6x + 36 \)[/tex]

B. [tex]\( y = x^2 + x + 18 \)[/tex]

C. [tex]\( y = 3x^2 - 6x + 45 \)[/tex]

D. [tex]\( y = x^2 - 6x + 45 \)[/tex]

Sagot :

GinnyAnswer
To convert the equation of a parabola from its vertex form to its standard form, let's start with the given vertex form:

[tex]\[ y = (x - 3)^2 + 36 \][/tex]

The next step is to expand the squared term:

[tex]\[ (x - 3)^2 \][/tex]

We can use the formula for expanding a binomial squared [tex]\((a - b)^2\)[/tex]:

[tex]\[ (x - 3)^2 = x^2 - 6x + 9 \][/tex]

Now, substitute this expanded form back into the original equation:

[tex]\[ y = x^2 - 6x + 9 + 36 \][/tex]

Next, we simplify the equation by combining like terms:

[tex]\[ y = x^2 - 6x + 45 \][/tex]

Hence, the standard form of the equation is:

[tex]\[ y = x^2 - 6x + 45 \][/tex]

From the given options, the correct answer is:

D. [tex]\( y = x^2 - 6x + 45 \)[/tex]
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