What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0)?
f(x) = (x - 2)(x-7)
f(x) = (x + 2)(x + 7)
f(x) = (x – 3)(x + 7)
f(x) = (x + 3)(x – 7)

 f(x) = (x + 3)(x – 7)

Step-by-step explanation:  Use "standard form" of the function and insert values given: vertex (2,-25) intercept point (7,0)

f(x) = a(x-h)² + k   from vertex, h is 2   y is -25   from intercept,  x is 7  f(x) is 0

to find a,  0 = a(7-2)² +(-25)   0 = a(7-2)² -25  add 25 to both sides

25 = a(5)²  25 = 25a  25/25 = a  1=a  (seems useless but verifies implied "a"coefficient is 1)

f(x) = a(x-h)² + k solve to get the quadratic form

f(x) = (x-2)² -25     (x - 2)² is x² -4x +4

f(x) = x² -4x +4 -25  simplify

f(x) = x² -4x - 21   then factor

f(x) = (x + 3)(x - 7)

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.