the equation:
[tex]y=x^2+18x-12[/tex]has the form:
[tex]y=ax^2+bx+c^{}[/tex]where a = 1, b = 18, and c= -12.
To complete the square, we need to add and subtract, the next term:
[tex](\frac{b}{2})^2[/tex]In this case:
[tex](\frac{18}{2})^2=9^2=81[/tex]Adding and subtracting 81 to the parabola, we get:
[tex]\begin{gathered} y=x^2+18x-12+81-81 \\ y=(x^2+18x+81)+(-12-81) \\ y=(x+9)^2-93 \end{gathered}[/tex]This equation has the form (the vertex form):
[tex]y=(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola. Then, the turning point (vertex) is (-9, -93)
