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)

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