Answer:
f(x) = 2(x –3)²
Step-by-step explanation:
f(x) = 2x² – 12x + 18
The vertex form of the above expression can be obtained as follow:
f(x) = 2x² – 12x + 18
Factorise
f(x) = 2(x² – 6x + 9)
Next, we shall simplify x² – 6x + 9 by factorisation method.
This is illustrated below:
x² – 6x + 9
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.
The factors are –3x and –3x
Next, replace –6x with –3x and –3x in the equation above as shown below:
x² – 6x + 9
x² – 3x –3x + 9
Factorise
x(x – 3) –3(x –3)
(x –3)(x –3)
(x –3)²
f(x) = 2x² – 12x + 18
f(x) = 2(x² – 6x + 9)
f(x) = 2(x –3)²
Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is
f(x) = 2(x –3)²
Answer:
Fred would have earned $31,022.31 after 16 years.
Step-by-step explanation:
To calculate compound interest, the initial capital must be multiplied by the interest rate applied to the capital, and in turn, this number must be exponential by the number of years that the investment lasts. Thus, in the case, the equation would be the following:
12.993 x (1 + 0.0559) ^ 16
In this way, multiplying the result exponentially by 16 years, the final compound interest would be $ 31,022.31.
Answer:
Therefore, the area of the ellipse is:
Area = 78.5 inches
Step-by-step explanation:
The formula to find the area of the ellipse is
The major axis of an ellipse = 25 inches
The minor axis of an ellipse = 4 inches
- The value of a = major axis/2 = 25/2 = 12.5 inches
- The value of b = minor axis/2 = 4/2 = 2 inches
Thus
The area of the ellipse:
Area =
inches ∵ 
Therefore, the area of the ellipse is:
Area = 78.5 inches
Answer:
A
Step-by-step explanation:
