The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. I
t goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
2 answers:
Answer:
The correct option is:
On the coordinate plane, there is a parabola that opens upwards, passing through the points (2, 10), having its vertex at (5, 1), and intersecting (8, 10).
Step-by-step explanation:
Initially, we must understand the translation rules
1) {f(x) + a} signifies f(x) moved up by (a) units
2) {f(x) – a} means f(x) moved down by (a) units
3) {f(x + a)} represents f(x) moved left by (a) units.
4) {f(x – a)} indicates f(x) moved right by (a) units.
Given information:
f(x) = x²
g(x) = (x-5)² + 1
By comparing the transformation from f(x) to g(x) with the translation rules
It can be concluded that g(x) represents f(x) through a translation of 5 units to the right and 1 unit upwards (rules 1 and 4)
Refer to the attached image, which illustrates the graphs of both f(x) and g(x)
As depicted, g(x) intersects (2, 10), has a vertex at (5, 1), and crosses through (8, 10)
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Answer:
A sum of $12,000 should be allocated at an interest rate of 5.25%, while $13,000 should be put in at 4%.
Step-by-step explanation:
Recall that
The simple interest formula is given by
where
I represents the total interest earned,
P is the initial investment,
r stands for the interest rate, and
t is the number of time periods.
Define
x as the amount invested at 5.25%,
and (25,000 - x) as the amount put in at 4%.
From the problem,
Plugging these into the formula:
Now, isolate x:
Hence, investing $12,000 at 5.25% and $13,000 at 4% meets the required interest condition.