Asked by Gupgupblupblupzorpzorpflapflap
Convert y = 2(x - 5)^2 - 10 to standard form.
Answers
Answered by
Gupgupblupblupzorpzorpflapflap
The 20 is incorrect
Answered by
GPT-4o mini
To convert the equation \( y = 2(x - 5)^2 - 10 \) to standard form, we need to expand the expression.
1. Start with the equation:
\[
y = 2(x - 5)^2 - 10
\]
2. Expand \((x - 5)^2\):
\[
(x - 5)^2 = x^2 - 10x + 25
\]
3. Substitute back into the equation:
\[
y = 2(x^2 - 10x + 25) - 10
\]
4. Distribute the 2:
\[
y = 2x^2 - 20x + 50 - 10
\]
5. Combine like terms:
\[
y = 2x^2 - 20x + 40
\]
Now the equation is in standard form \( y = ax^2 + bx + c \), where \( a = 2 \), \( b = -20 \), and \( c = 40 \).
Thus, the standard form of the equation is:
\[
y = 2x^2 - 20x + 40
\]
1. Start with the equation:
\[
y = 2(x - 5)^2 - 10
\]
2. Expand \((x - 5)^2\):
\[
(x - 5)^2 = x^2 - 10x + 25
\]
3. Substitute back into the equation:
\[
y = 2(x^2 - 10x + 25) - 10
\]
4. Distribute the 2:
\[
y = 2x^2 - 20x + 50 - 10
\]
5. Combine like terms:
\[
y = 2x^2 - 20x + 40
\]
Now the equation is in standard form \( y = ax^2 + bx + c \), where \( a = 2 \), \( b = -20 \), and \( c = 40 \).
Thus, the standard form of the equation is:
\[
y = 2x^2 - 20x + 40
\]