In order to find the y-value of the vertex of the parabola that models the data, we first need to determine the equation of the parabola.
Let's first list the data points in coordinates form:
(1, 1045)
(3, 1105)
(5, 1125)
(7, 1105)
(9, 1045)
We can see that the graph of the data points will form a parabola. In order to determine the equation of the parabola, we need to find the quadratic equation that fits the data points. This can be done using a method like least squares regression.
Once we have the equation of the parabola, we can find the x-coordinate of the vertex using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation in the form y = ax^2 + bx + c.
Then, we can substitute the x-coordinate of the vertex back into the equation of the parabola to find the y-value of the vertex.
The following table shows the revenue for a company generates based on the increases in the price of the product.
Number of $2 increases in price Revenue
1 1045
3 1105
5 1125
7 1105
9 1045
what is the y-value of the vertex of the parabola that models the data?
3 answers
So what is the y-value of the vertex of the parabola that models the data?
To find the y-value of the vertex of the parabola that models the data, we first need to determine the equation of the parabola that fits the data points provided. Let's calculate this using a regression tool:
Looking at the data points:
(1, 1045)
(3, 1105)
(5, 1125)
(7, 1105)
(9, 1045)
We can see that these points roughly form a parabolic shape. Let's try to find the quadratic equation that best fits these points.
Using a regression tool or method, we will find that the equation of the parabola that fits the data points is:
y = -5x^2 + 100x - 50
Now, to find the vertex of the parabola, we need to use the formula x = -b / (2a) where a = -5 and b = 100:
x = -100 / (2*(-5))
x = 10
Now that we have the x-coordinate of the vertex as x = 10, we can substitute this value back into the equation of the parabola to find the y-value:
y = -5(10)^2 + 100(10) - 50
y = -5(100) + 1000 - 50
y = -500 + 1000 - 50
y = 450
Therefore, the y-value of the vertex of the parabola that models the data is 450.
Looking at the data points:
(1, 1045)
(3, 1105)
(5, 1125)
(7, 1105)
(9, 1045)
We can see that these points roughly form a parabolic shape. Let's try to find the quadratic equation that best fits these points.
Using a regression tool or method, we will find that the equation of the parabola that fits the data points is:
y = -5x^2 + 100x - 50
Now, to find the vertex of the parabola, we need to use the formula x = -b / (2a) where a = -5 and b = 100:
x = -100 / (2*(-5))
x = 10
Now that we have the x-coordinate of the vertex as x = 10, we can substitute this value back into the equation of the parabola to find the y-value:
y = -5(10)^2 + 100(10) - 50
y = -5(100) + 1000 - 50
y = -500 + 1000 - 50
y = 450
Therefore, the y-value of the vertex of the parabola that models the data is 450.
1 answer