lizziefufu2
Answered

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Question 4 of 10:

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][tex]$y=x^2-6x+45$[/tex][/tex]
B. [tex]$y=3x^2-6x+45$[/tex]
C. [tex]$y=x^2+x+18$[/tex]
D. [tex][tex]$y=x^2+6x+36$[/tex][/tex]

Sagot :

GinnyAnswer
To convert the given vertex form of the parabola equation [tex]\( y = (x - 3)^2 + 36 \)[/tex] into the standard form, we need to follow these steps:

1. Expand the squared term [tex]\((x - 3)^2\)[/tex]:
[tex]\[ (x - 3)^2 = x^2 - 6x + 9 \][/tex]

2. Substitute the expanded form back into the equation:
[tex]\[ y = x^2 - 6x + 9 + 36 \][/tex]

3. Combine like terms:
[tex]\[ y = x^2 - 6x + 9 + 36 \][/tex]
[tex]\[ y = x^2 - 6x + 45 \][/tex]

So, the standard form of the equation is:
[tex]\[ y = x^2 - 6x + 45 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{A. \, y = x^2 - 6x + 45} \][/tex]
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