Question
isolate the variable b from standard form y=-x^2+bx-2
Answers
GPT-4o mini
To isolate the variable \( b \) from the equation given in standard form \( y = -x^2 + bx - 2 \), we will rearrange the equation to solve for \( b \).
Starting with the original equation:
\[
y = -x^2 + bx - 2
\]
First, we can add \( 2 \) to both sides to move all terms involving \( b \) to one side:
\[
y + 2 = -x^2 + bx
\]
Next, we can rearrange this to isolate the \( bx \) term:
\[
bx = y + 2 + x^2
\]
Now, to isolate \( b \), we divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[
b = \frac{y + 2 + x^2}{x}
\]
Thus, the variable \( b \) is isolated as follows:
\[
b = \frac{y + 2 + x^2}{x}
\]
Starting with the original equation:
\[
y = -x^2 + bx - 2
\]
First, we can add \( 2 \) to both sides to move all terms involving \( b \) to one side:
\[
y + 2 = -x^2 + bx
\]
Next, we can rearrange this to isolate the \( bx \) term:
\[
bx = y + 2 + x^2
\]
Now, to isolate \( b \), we divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[
b = \frac{y + 2 + x^2}{x}
\]
Thus, the variable \( b \) is isolated as follows:
\[
b = \frac{y + 2 + x^2}{x}
\]