Answer:
D.) g(x) = -x² - 3
Step-by-step explanation:
The function was shifted 3 down...
x² ↓ 3 = x² - 3
and inverted, giving you this:
-1 · x² - 3 = -x² - 3
<em>g(x) = -x² - 3</em>
To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c.
We are given two different solutions of the equation.
First, (2, 0).
Second, (0, 14).
So we have a value (14) for c. We can substitute that into our first equation to find b.
We can now plug in our values for b and c into the equation to get its standard form.
To find the vertex, we can convert this equation to vertex form
by completing the square.
Thus, the vertex is (4.5, –6.25).
We can confirm the solution graphically (see attachment).
Answer: x=1 my friend
Step-by-step explanation:
Answer: The equilibrium point is where; Quantity supplied = 100 and Quantity demanded = 100
Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.
The supply function is given as
S(q) = (q + 6)^2
The demand function is given as
D(q) = 1000/(q + 6)
The equilibrium point therefore would be derived as
(q + 6)^2 = 1000/(q + 6)
Cross multiply and you have
(q + 6)^2 x (q + 6) = 1000
(q + 6 )^3 = 1000
Add the cube root sign to both sides of the equation
q + 6 = 10
Subtract 6 from both sides of the equation
q = 4
Therefore when q = 4, supply would be
S(q) = (4 + 6)^2
S(q) = 10^2
S(q) = 100
Also when q = 4, demand would be
D(q) = 1000/(4 + 6)
D(q) = 1000/10
D(q) = 100
Hence at the point of equilibrium the quantity demanded and quantity supplied would be 100 units.
B is a translation, which is moving.
A is a rotation, and C is a reflection over the x-axis.