Write a quadratic function in vertex form with a vertex at (-4,2)

y = ( x + 4 ) ^ 2 + 2

Step-by-step explanation:

vertex form of quadradtic is:

y = a ( x − h ) ^ 2 + k

with vertex (-4,2) = (h,k)

y = a ( x − (-4) ) ^ 2 + 2

y = a ( x + 4 ) ^ 2 + 2

'a' can be any non-zero real value

say a = 1

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %