Match each quadratic graph to its respective function
1 answer:
Answer:
f(x) = (x - 3)(x + 1) → Corresponds with the first (raised higher ) ∪ shaped graph
f(x) = -2(x - 1)((x + 3) → Corresponds with the ∩ shaped graph
f(x) = 0.5(x - 6)((x + 2) → Corresponds with the second (lower) ∪ shaped graph
Step-by-step explanation:
For the function f(x) = (x - 3)(x + 1)
We have;
When x = 0, y = -3
When y = 0 x = 3 or -1
Comparing with the graphs, it best suits the first ∪ shaped graph that rises here than the other ∪ shaped graph
For the function;
f(x) = -2(x - 1)((x + 3)
When x = 0, y = 6
When y = 0, x = 1 or -3
Which corresponds with the ∩ shaped graph
For the function;
f(x) = 2(x + 6)((x - 2)
When x = 0, y = -24
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = 0.5(x - 6)((x + 2)
When x = 0, y = -6
When y = 0, x = 6 or -2
Which best suits the second ∪ shaped graph that is lower than the other (first) ∪ shaped graph
For the function;
f(x) = 0.5(x + 6)((x - 2)
When x = 0, y = -6
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = (x + 3)((x - 1)
When x = 0, y = -3
When y = 0, x = -3 or 1
Graph not included
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2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
Answer:
a)
The function that represents the value of the account at any time, t
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.
Step-by-step explanation:
a. Write the function that represents the value of the account at any time, t.
The function that represents the value of the account at any time, t
where
A represents the Future Value
P represents the Principle (Initial Value)
r represents the Interest rate
t represents the time
b) What will the value be after 6 years?
Given
The principal amount P = $5500
Annual Rate r = 3.75% = 3.75/100 = 0.0375
Time Period t = 6 years
To Determine:
The total amount A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.