The general equation of a parabola with vertex (h,k) is
[tex]y=C(x-h)^2+k[/tex]In our case, we have h = 13 and k =6. So we get the equation
[tex]y=C(x-13)^2+6[/tex]Now, to find the value of C, we will use the given y intercept. In the previous equation we should get y=19 if we replace x = 0. So
[tex]19=C(-13)^2+6\text{ = 169C + 6}[/tex]If we subtract 6 on both sides, we get
[tex]19\text{ - 6 = 13 = 169 C}[/tex]If we divide both sides by 169, we get
[tex]C\text{ = }\frac{13}{169}\text{ = }\frac{1}{13}[/tex]So the general equation of the given quadratic function is
[tex]y\text{ = }\frac{1}{13}(x-13)^2+6[/tex]