Energy Use Light Output
35 2250
50 4000
70 5800
100 9500
150 16000
What is the quadratic model for the light output with respect to use energy use?
I don't understand this at all Please help ):
To find the quadratic model for the light output with respect to energy use, we need to fit a quadratic equation to the given data points. A quadratic equation is in the form of y = ax^2 + bx + c, where y represents the light output and x represents the energy use.
To begin, let's represent the energy use as x and the light output as y. We have the following data points:
(35, 2250)
(50, 4000)
(70, 5800)
(100, 9500)
(150, 16000)
We can use these points to derive the quadratic equation by following these steps:
Step 1: Substitute the values of x and y into the quadratic equation: y = ax^2 + bx + c.
Using the first data point (35, 2250), we get:
2250 = a(35)^2 + b(35) + c
Step 2: Repeat this process for the other data points, substituting the values of x and y into the equation.
Using the second data point (50, 4000), we get:
4000 = a(50)^2 + b(50) + c
Using the third data point (70, 5800), we get:
5800 = a(70)^2 + b(70) + c
Using the fourth data point (100, 9500), we get:
9500 = a(100)^2 + b(100) + c
Using the fifth data point (150, 16000), we get:
16000 = a(150)^2 + b(150) + c
Step 3: Solve the resulting system of equations simultaneously. This will give us the values of a, b, and c, which can be used to form the quadratic equation.
Once you solve the system of equations, you will have the values of a, b, and c, which can be used to write the quadratic equation for the given data.
Remember, the quadratic equation is of the form:
y = ax^2 + bx + c
By finding the values of a, b, and c, you can fill in the equation and obtain the quadratic model for the light output with respect to energy use.