Given:
[tex]y=-2(x+7)^2+13[/tex]
Let's solve the equation for x.
• Re-arrange the equation:
[tex]-2(x+7)^2+13=y[/tex]
• Subtract 13 from both sides of the equation:
[tex]\begin{gathered} -2(x+7)^2+13-13=y-13 \\ \\ -2(x+7)^2=y-13 \end{gathered}[/tex]
• Divide both sides by -2:
[tex]\begin{gathered} \frac{-2(x+7)^2}{-2}=\frac{y-12}{-2} \\ \\ (x+7)^2=\frac{y-13}{-2} \end{gathered}[/tex]
• Take the square root of both sides:
[tex]\begin{gathered} \sqrt{(x+7)^2}=\sqrt{\frac{y-13}{-2}} \\ \\ x+7=\sqrt{\frac{y-13}{-2}} \end{gathered}[/tex]
• Subtract 7 from both sides of the equation:
[tex]\begin{gathered} x+7-7=\sqrt{\frac{y-13}{-2}}-7 \\ \\ x=\sqrt{\frac{y-13}{-2}}-7 \end{gathered}[/tex]
ANSWER:
[tex]x=\sqrt{\frac{y-13}{-2}}-7[/tex]
