The vertex form of the equation of a parabola is given by
[tex]y-k=a(x-h)^2[/tex]
where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is (-12, -2), the equation of the parabola is given by
[tex]y-(-2)=a(x-(-12))^2 \\ \\ y+2=a(x+12)^2=a(x^2+24x+144)=ax^2+24ax+144a \\ \\ y=ax^2+24ax+114a-2 \\ \\ y=x^2+24x+ \frac{114a-2}{a} [/tex]
For a = 1,
[tex]y=x^2+24x+112[/tex]
The
parabola whose minimum is at (−12,−2) is given by the equation [tex]y=x^2+ax+b[/tex], where a = 24 and b = 112.
