<span>f(x) = one eighth (x - 2)^2 - 1
Since a parabola is the curve such that all points on the curve have the same distance from the directrix as the distance from the point to the focus.With that in mind, we can quickly determine 3 points on the parabola. The 1st point will be midway between the focus and the directrix, So:
(2, (1 + -3)/2) = (2, -2/2) = (2,-1).
The other 2 points will have the same y-coordinate as the focus, but let offset on the x-axis by the distance from the focus to the directrix. Since the distance is (1 - -3) = 4, that means the other 2 points will be (2 - 4, 1) and (2 + 4, 1) which are (-2, 1) and (6, 1). The closest point to the focus will have the same x-coordinate as the focus, so the term will be (x-2)^2. This eliminates the functions "f(x) = -one eighth (x + 2)^2 - 1" and "f(x) = -one half (x + 2)^2 - 1" from consideration since their x term is incorrect, leaving only "f(x) = one eighth (x - 2)^2 - 1" and "f(x) = one half (x - 2)^2 + 1" as possible choices. Let's plug in the value 6 for x and see what y value we get from squaring (x-2)^2. So:
(x-2)^2
(6-2)^2 = 4^2 = 16
Now which option is equal to 1? Is it one eighth of 16 minus 1, or one half of 16 plus 1?
16/8 - 1 = 2 - 1 = 1
16/2 + 1 = 8 + 1 = 9
Therefore the answer is "f(x) = one eighth (x - 2)^2 - 1"</span>
When you’re younger, it’s not so much about the type of investments you hold but more about just diligently saving. “Mutual funds or stocks? It just doesn’t matter much at this stage,” says certified financial planner Janet Gray. “Simply having a savings account means you’re in the game.”
That’s because at the beginning, your savings will be the key way of growing your money. “So don’t focus on being an investment expert early on,” says investment manager Dan Bortolotti. “Focus on frugal living and adding even small amounts, like an extra $50 or more a month, to your savings. That goes a long way over time so be patient and focus on savings.” In these early years, just celebrate the fact that you actually have money and are growing your wealth in a disciplined way. “You’re ahead of a lot of people,” says Gray.
The lengths of the segments can be calculated using:
d = √[(y₂-y₁)² + (x₂-x₁)]²
First, we calculate the length of AB using this formula:
L(AB) = 10
Then, we calculate the length of A'B':
L(A'B') = 3
Therefore, the scale factor is: L(A'B') / L(AB) = 3/10
Answer:
225 cm²
Step-by-step explanation:
The ratio of areas is the square of the scale factor.
area UVW = (5/2)²·area RST = (25/4)(36 cm²) = 225 cm²
