Problem
write a quadratic function whose graph passes through (4,-7) and has a vertex of (1,-6) what does y=
Solution
the general equation of a parabola is given by:
y-k = a(x-h)^2
And for this case the vertex is given by:
V = (h= 1, k = -6)
And then we have this:
y- (-6)= a(x-1)^2
y+6 = a(x-1)^2
Now we can use the point given x= 4 and y= -7 and we can solve for a and we got:
-7+6 = a(4-1)^2
-1= a(3)^2
a= -1/9
And then the final solution would be:
y= -1/9 (x-1)^2 - 6