lizziefufu2
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Ask your questions and receive precise answers from experienced professionals across different disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.