Question

Express y + x^2=x + 6 in the form
y=ax^2 + bx + c

Answer 1

To express the equation \( y + x^2 = x + 6 \) in the form \( y = ax^2 + bx + c \), we need to isolate \( y \).

Starting with the given equation:

\[
y + x^2 = x + 6
\]

Subtract \( x^2 \) from both sides to solve for \( y \):

\[
y = x + 6 - x^2
\]

Now, we can rearrange the right-hand side:

\[
y = -x^2 + x + 6
\]

This expression is now in the form \( y = ax^2 + bx + c \), where:

- \( a = -1 \)
- \( b = 1 \)
- \( c = 6 \)

So the equation can be expressed as:

\[
y = -1x^2 + 1x + 6
\]

or simply:

\[
y = -x^2 + x + 6
\]