The function h(x)=1/2(x+3)^2+2. how is the graph of h(x) translated from the parent graph of a quadratic function, f(x)=x^2? select all that apply. a. the graph of h(x) is shifted 3 units to the right of the parent graph. b. the graph of h(x) is shifted 2 units up from the parent graph. c. the graph of h(x) is vertically compressed by a factor of 1/2 d. the graph of h(x) is a reflection of the parent graph. e. the graph of h(x) has a different y-intercept from the parent graph. f. both graphs have two x intercepts.

B. The graph of h(x) is shifted 2 units up from the parent graph;  C. The graph of h(x) is vertically compressed by a factor of 1/2 ;   E. The graph of h(x) has a different y-intercept from the parent graph.

Step-by-step explanation:

Adding 3 to the variable x before the exponent is applied shifts the graph horizontally.  Since it is added, this means it is shifted 3 units to the left, not the right.

Adding 2 to the end of the function shifts the graph vertically.  Since it is added, it is shifted 2 units up.

Multiplying the function by 1/2 compresses it vertically by a factor of 1/2.

These graphs are not reflections, and neither graph has two x-intercepts.

The two graphs do have different y-intercepts.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.