Certainly! Let's write the equation [tex]\( y = (x-3)^2 - 25 \)[/tex] in standard form. We will go through the steps systematically:
1. Expand the squared term:
[tex]\[
(x - 3)^2
\][/tex]
To expand this, we use the formula [tex]\( (a - b)^2 = a^2 - 2ab + b^2 \)[/tex]:
[tex]\[
(x - 3)^2 = x^2 - 6x + 9
\][/tex]
2. Substitute the expanded form back into the original equation:
[tex]\[
y = x^2 - 6x + 9 - 25
\][/tex]
3. Simplify the constants:
[tex]\[
y = x^2 - 6x + 9 - 25
\][/tex]
Combine the constant terms:
[tex]\[
y = x^2 - 6x - 16
\][/tex]
4. Set the equation to zero to get it in standard form:
[tex]\[
x^2 - 6x - 16 = 0
\][/tex]
So, the standard form of the equation [tex]\( y = (x-3)^2 - 25 \)[/tex] is:
[tex]\[
x^2 - 6x - 16 = 0
\][/tex]
