Answer:
f(x) = x² - 9
Step-by-step explanation:
Given x = a is a zero of the polynomial f(x) then (x - a) is a factor
Given zeros are x = 3 and x = - 3, then corresponding factors are
(x - 3) and (x - (- 3) ), that is
(x - 3) and (x + 3)
The function is then the product of the factors, that is
f(x) = (x - 3)(x + 3) ← expand using FOIL
f(x) = x² - 9
The key is Esther travelled the same distance - x - in both her morning and evening commute.
45(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x
Therefore 45(p) = 30(q), or divide both sides by 5 and get 9(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.
Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.
Therefore 9(60-q) = 6q or 540-9q = 6q. So 540 = 15q, which makes q = 36. If q = 36, then by (p+q)=60, p (the time she took in the morning) must equal 24.
45 miles per hour, her speed in the morning, times (24/60) hours, her time, makes 18 miles travelled in the morning. If you check, 30 miles per hour times (36/60) hours also makes 18 miles in the evening.
<span>Hope that makes a little sense. And I also hope it's right</span>
Step-by-step explanation:
need the graph
but, it will cross y axis at 3 and line will be going down
