Hello Kamaiya,
The vertex form of the equation of a parabola: y = a *(x-h)2 + k where:
h is the x-coordinate of the vertex; k is the y-coordinate of the vertex
Let's plug them in to the above equation: y = a *(x- -3)2 + 6 so y = a *(x + 3)2 + 6
You're also given a point (1,-2) that's on that parabola, so now replace the x and y from the equation by 1 and -2 respectively:
-2 = a *(1 + 3)2 + 6 ---> -2 = a *(4)2 + 6 ----> -2 = a *16 + 6
We're now looking to solve for a. Subtract 6 from both sides: -8 = a*16
Divide both sides by 16: -8/16 = a -------> a = -1/2
Therefore, the equation of the parabola with vertex (-3,6) and point (1,-2) is:
y = (-1/2)*(x + 3)2 + 6
Quick check: replace x and y by 1 and -2 and compare both sides of the equation:
-2 = (-1/2)*(1+3)2 + 6 = (-1/2)*(4)2 + 6 = (-1/2)*16 + 6 = -8 + 6 = -2
-2 = -2 so the equation is correct :)
