Question

Standard form of y= -6(x+8)^2-10

Answer 1

To convert the equation \( y = -6(x + 8)^2 - 10 \) into standard form, we will expand and simplify it.

1. Start with the given equation:
\[
y = -6(x + 8)^2 - 10
\]

2. Expand \( (x + 8)^2 \):
\[
(x + 8)^2 = x^2 + 16x + 64
\]

3. Substitute back into the equation:
\[
y = -6(x^2 + 16x + 64) - 10
\]

4. Distribute \(-6\):
\[
y = -6x^2 - 96x - 384 - 10
\]

5. Combine like terms:
\[
y = -6x^2 - 96x - 394
\]

Now, the standard form of the equation \( y = -6x^2 - 96x - 394 \) can be written as:
\[
y = -6x^2 - 96x - 394
\]

This is in the standard form \( y = ax^2 + bx + c \) where \( a = -6 \), \( b = -96 \), and \( c = -394 \).