1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.
Y = 7.5*200 +500
y = 1500 +500
y = 2000
2000 gallons are in the pool 200 minutes after the pump is turned on.
Answer:
The cost of the pillar is $22,947.12
Step-by-step explanation:
Diameter of the pillar = 6m
Radius = diameter / 2 = 6 / 2 = 3m
Height if the pillar = 7m
Volume of the pillar = πr²h
π = 3.14
V = 3.14 × 3² × 7
V = 3.14 × 9 × 7
V = 197.82m³
Volume of the pillar is 197.82m³
If 1m³ = $116
197.82m³ will cost $x
X = (197.82 × 116) / 1
X = $22,947.12
The cost of the pillar is $22,947.12
