How do you find the equation of a parabola with x intercepts -1 and 3 and y intercept 8?

Steps

1) Find the co-ordinates of the vertex, by adding the x-intercepts and dividing by 2.


Xv= (-1+3) / 2


This gives you the x-coordinate of the vertex, 1. The vertex of the parabola is at (1, 8)


2) Sub into the vertex form equation. (y= a(x-h)2+k h = x coord of vertex, k = y coord


y=a(x-1)2+8


note: when subbing in x value, always put the reverse sign into the equation, if positive, sub it in as negative, if negative, sub in as positive


Now you can't solve for a without knowing what point is passes through on the y-axis. after you know that you just solve sub x and y in, solve for a, then put a into the equation


ex: y= 2(x-1)2+8