The graphs below have the same shape. What is the equation of the blue
1 answer:
Answer:
Option C.
Step-by-step explanation:
The complete question in the attached figure
we know that
The equation of the function f(x) is
Is a parabola open upward
The vertex is the point (0,0)
The function g(x) have the same shape
The vertex of the function g(x) is the point (-3,1)
so
The rule of the transformation of f(x) to g(x) is
(0,0) -----> (-3,1)
(x,y) -----> (x-3,y+1)
That means----> The translation is 3 units at left and 1 unit up
therefore
The equation of the function g(x) in vertex form is equal to
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Part A:
Given that <span>Victor is buying a home for $125,340 and that he is making a 15% down payment.
The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.
Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539
Part B
</span>Given that he earns a gross annual income of $64,570 <span>and that the loan of $106,539 will be spread for 20 years at 3.75% interest.
$106,539 / 20 = $5,326.95
Roughly he will be paying about $5,000 every year which is way below his annual gross income.
Therefore, he can afford the mortgage.
Part C
The monthly mortgage payment can be calculated using the present value of annuity formula given by
</span>
<span>
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.
Here, PV = </span>$106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.
Thus, we have:
Therefore, the monthly mortgage payment is $631.66
Part D
Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40
Therefore, his total payment for the house will be $151,598.40
Part E
Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.
Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40
Given that <span>Victor is buying a home for $125,340 and that he is making a 15% down payment.
The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.
Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539
Part B
</span>Given that he earns a gross annual income of $64,570 <span>and that the loan of $106,539 will be spread for 20 years at 3.75% interest.
$106,539 / 20 = $5,326.95
Roughly he will be paying about $5,000 every year which is way below his annual gross income.
Therefore, he can afford the mortgage.
Part C
The monthly mortgage payment can be calculated using the present value of annuity formula given by
</span>
<span>
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.
Here, PV = </span>$106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.
Thus, we have:
Therefore, the monthly mortgage payment is $631.66
Part D
Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40
Therefore, his total payment for the house will be $151,598.40
Part E
Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.
Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40