Explanation:
Mathematics Capabilities.
Can you do math?
ChatGPT
Yes, I am capable of doing math. As an AI language model, I can perform mathematical operations and solve mathematical problems using algorithms and programming logic. However, my abilities are limited to the mathematical knowledge and programming that I have been trained on, which is primarily focused on the types of mathematics that are typically encountered in everyday life and academic settings.
X. g(x) -2. -6 -1. 10 0. 18 1. 16 Which quadratic function best represent the data below? g(x)= -2.25 + 78.5 + 19.05 g(x)= -4.5x^2 + 2.9x + 17.7 g(x)= -5.5x^2 + .7x + 17.1 g(x)= -2.9x^2 + 4.5x + 17.7
ChatGPT
To determine which quadratic function best represents the data, we can plug in the given values of x and g(x) into each equation and see which one produces the closest values to the given data.
Using the first equation,
g(-2) = -2.25(-2)^2 + 78.5(-2) + 19.05 = -30.1 g(-1) = -2.25(-1)^2 + 78.5(-1) + 19.05 = -9.9 g(0) = -2.25(0)^2 + 78.5(0) + 19.05 = 19.05 g(1) = -2.25(1)^2 + 78.5(1) + 19.05 = 95.3
Using the second equation,
g(-2) = -4.5(-2)^2 + 2.9(-2) + 17.7 = -5.1 g(-1) = -4.5(-1)^2 + 2.9(-1) + 17.7 = 15.1 g(0) = -4.5(0)^2 + 2.9(0) + 17.7 = 17.7 g(1) = -4.5(1)^2 + 2.9(1) + 17.7 = 15.1
Using the third equation,
g(-2) = -5.5(-2)^2 + .7(-2) + 17.1 = -34.7 g(-1) = -5.5(-1)^2 + .7(-1) + 17.1 = -7.9 g(0) = -5.5(0)^2 + .7(0) + 17.1 = 17.1 g(1) = -5.5(1)^2 + .7(1) + 17.1 = 11.3
Using the fourth equation,
g(-2) = -2.9(-2)^2 + 4.5(-2) + 17.7 = -30.9 g(-1) = -2.9(-1)^2 + 4.5(-1) + 17.7 = 10.3 g(0) = -2.9(0)^2 + 4.5(0) + 17.7 = 17.7 g(1) = -2.9(1)^2 + 4.5(1) + 17.7 = 19.3
Comparing the calculated values with the given data, we see that the third equation, g(x) = -5.5x^2 + 0.7x + 17.1, produces the closest values to the given data. Therefore, the quadratic function that best represents the data is g(x) = -5.5x^2 + 0.7x + 17.1.