F A taxicab company charges $2.80 plus $0.40 per mile. Carmen paid a fare of $8.80. Enter and solve an equation to find the numb
2 answers:
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Part A
After dividing the first two terms by the coefficient of n², the coefficient of the linear term is -6, so we can complete the square by adding (and subtracting) the square of half that: (-6/2)² = 9.
... g(n) = n² -6n + 9 + 16 - 9
... g(n) = (n -3)² +7 . . . . . . . rewrite to vertex form
Part B
The generic vertex form is
... y = a(x -h)² +k . . . . . . for vertex (h, k) and vertical expansion factor "a"
Comparing this to g(n), we see a=1, h=3, k=7. When a > 0, the parabola opens upward, and the vertex is a minimum. Here, we have a > 0, so we can conclude ...
... the vertex (3, 7) is a minimum
Part C
The axis of symmetry is the vertical line through the vertex.
... x = 3
You can use the distance formula:
To figure out what the distance between the points is. Our x1 is -1, and our y1 is 3. Our x2 is 7, and our y2 is -3. Then, we can just plug it in, and solve:
Simplify:
Simplify Further (S is the distance):
So, the answer is D, 8 units. If you want me to explain what I did, just tell me, I sure will! :) Anything still unclear?
To figure out what the distance between the points is. Our x1 is -1, and our y1 is 3. Our x2 is 7, and our y2 is -3. Then, we can just plug it in, and solve:
Simplify:
Simplify Further (S is the distance):
So, the answer is D, 8 units. If you want me to explain what I did, just tell me, I sure will! :) Anything still unclear?