The equation of the parabola with vertex (h,k)(h,k) is y=a(−h+x)^2+ky=a(−h+x)^2+k.
Thus, the equation of the parabola is y=a(x+3)^2+1y=a(x+3)^2+1.
To find a, use the fact that the parabola passes through the point (−2,4)(−2,4): 4=a+14=a+1.
Solving this equation, we get that a=3a=3.
Thus, the equation of the parabola is y=3(x+3)2+1y=3(x+3)^2+1.
I used parabola calculator.
Hope it helps!