The work is illustrated and shown.
Answer:
Answer choice C. 
.
Step-by-step explanation:
The entire question is present in the attached figure.
It is established that
The function f(x) is represented by
,
indicating a parabola that opens upward.
The vertex is situated at the point (0,0).
The function g(x) shares the same parabolic shape.
The vertex of g(x) is located at (-3,1).
Therefore,
The transformation from f(x) to g(x) can be described as:
(0,0) transforms to (-3,1).
(x,y) transforms to (x-3,y+1).
This indicates a shift of 3 units to the left and 1 unit upward.
Thus,
The equation for g(x) in vertex form can be expressed as
.
Honestly, I find Mrs. Garcia's method easier to perform mentally. It hinges on how familiar you are with your multiples of 5. (5*15 = 75 is a multiplication I often use)
Melissa's approach involves calculating 5*20 = 100 and 5*9 = 45, then combines the 3-digit result 100 with the 2-digit result 45, yielding 145. Adding 45 to 00 is simple and doesn’t require carrying digits, thus the arithmetic is fairly straightforward.
Mrs. Garcia's technique involves computing 5*14 = 70 and 5*15 = 75, then summing these two-digit results. Many people may not readily recall that 5*15=75, which complicates forming that product. The addition of 70 and 75 requires a carrying operation, making the math somewhat more complex. The resulting total is 145.
(The rationale behind my preference for Mrs. Garcia's method is that I can achieve the final sum by simply doubling 7 tens, followed by adding 5. The only 3-digit number to remember mentally is the ultimate total.)
_____Subtraction introduces a slight complication, yet reshaping it as $5(30 -1) = $150 - 5 = $145 is possible.
Or, you may reframe it as $5(28 +1) = $140 +5 = $145.
Dividing an even number by 2 to find the product of 5 is straightforward when you append a zero.
5*14 = 10*7 = 70
5*28 = 10*14 = 140.
