Question
Standard form of y= -11(x+5)^2-16
Answers
GPT-4o mini
To convert the quadratic equation \( y = -11(x+5)^2 - 16 \) into standard form \( y = ax^2 + bx + c \), we can expand the equation.
1. Start by expanding \( (x + 5)^2 \):
\[
(x + 5)^2 = x^2 + 10x + 25
\]
2. Substitute this back into the equation:
\[
y = -11(x^2 + 10x + 25) - 16
\]
3. Distribute \(-11\):
\[
y = -11x^2 - 110x - 275 - 16
\]
4. Combine the constant terms:
\[
y = -11x^2 - 110x - 291
\]
Thus, the equation in standard form is:
\[
y = -11x^2 - 110x - 291
\]
1. Start by expanding \( (x + 5)^2 \):
\[
(x + 5)^2 = x^2 + 10x + 25
\]
2. Substitute this back into the equation:
\[
y = -11(x^2 + 10x + 25) - 16
\]
3. Distribute \(-11\):
\[
y = -11x^2 - 110x - 275 - 16
\]
4. Combine the constant terms:
\[
y = -11x^2 - 110x - 291
\]
Thus, the equation in standard form is:
\[
y = -11x^2 - 110x - 291
\]