Question

Write a quadratic function whose graph passes through (4,-7) and has a vertex of (1,-6) what does y=

Answer 1

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