What does it mean by, Use the given zeros to write the complete factored form of f(x)

Question

f(x) = 2x^2-25x+77; zeros: 11/2 and 7

Answer 1

2x^2 -25x + 77

= (x-7)(x-11/2)2 in factored form, take each zero, change its sign and stick an x in front of it to get the two variable factors. Add a 2 to make the x^2 term into 2x^2

2(7)^2-25(7)+77=0

2(11/2)^2 -25(11/2) + 77 = 0

half way between the two zeros is the x coordinate of the vertex

7+5.5 = 12.5. Divide by 2 to get 6 1/4 or 6.25, the axis of symmetry is x=6.25

2(6.25)^2 -25(6.25) + 77 = - 1 1/8 = -1.125 vertex is (6.25, -1.125)

f(x) = 2(x-6.25)^2 - 1.125 is another factored standard vertex form

2(7-6.25)^2 -1.125 = 2(.75)^2 - 1.125 = 2(.5625) -1.125 = 1.125-1.125 = 0