Answer:
Step-by-step explanation:
The first parabola has vertex (-1, 0) and y-intercept (0, 1).
We plug these values into the given vertex form equation of a parabola:
y - k = a(x - h)^2 becomes
y - 0 = a(x + 1)^2
Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:
1 = a(0 + 1)^2, and from this we know that a = 1. Thus, the equation of the first parabola is
y = (x + 1)^2
Second parabola: We follow essentially the same approach. Identify the vertex and the two horizontal intercepts. They are:
vertex: (1, 4)
x-intercepts: (-1, 0) and (3, 0)
Subbing these values into y - k = a(x - h)^2, we obtain:
0 - 4 = a(3 - 1)^2, or
-4 = a(2)². This yields a = -1.
Then the desired equation of the parabola is
y - 4 = -(x - 1)^2
Answer:
See answer below
Step-by-step explanation:
For the first expression
3 x (x - 2) + 2 = 3 x^2 - 6 x + 2
evaluated at x= 4 we get: 26
and for x = 5 we get 47.
For the second expression
2 x^2 + 3 x - 18
we get the exact same values when doing the evaluation at these two points.
Based on those results, one may think the expressions may be equivalent, but they are not equivalent. Because at any other x-value, their results are different. See for example that for x = 0 the first one gives "2" while the second one gives -18.
Answer:
its the 3rd one
Step-by-step explanation:
Answer:
R(x) =300·x - 2·x²
C(x) = £5000 + £40 × x
The break even points are 23.47 and 106.53 or 23 and 107 bikes
Step-by-step explanation:
Given that the price function P(x) = 300 -2·x
Cost per bike = £40
The revenue function R(x) is given by bike price × total number of bikes manufactured and sold
∴ R(x) = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²
The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced
∴ C(x) = £5000 + £40 × x
The break even point is given by the relation;
Total revenue - total cost = 0
That is, break even point is R(x) - C(x) = 0
300·x - 2·x² - (5000 + 40·x) = 0
-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0
Factorizing, we have;
(x - (65 -5√69))(x - (65 +5√69))
Solving gives x = 23.47 or 106.53
Therefore, the break even points are 23.47 and 106.53.
That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.
