Question

Write a quadratic function with a graph that meets the following conditions: x-intercepts at (2, 0) and (6, 0) with a minimum at (4, -8)

Answer 1

the minimum is the vertex
y=a(x-h)^2+k
(h,k) is vertex
given
(4,-8)
y=a(x-4)^2-8
find a
given
(2,0) and (6,0)
find a

0=a(2-4)^2-8
0=a(2)^2-8
0=4a-8
8=4a
divide 4
2=a

other one
0=a(6-4)^2-8
0=a(2)^2-8
0=4a-8
8=4a
divide 4
2=a


the function is
y=2(x-4)²-8 or expanded
y=2x^2-16x+24