Given the quadratic regression model 𝑦 is equal to negative 𝑥 squared plus 5.2𝑥 minus 2.1, calculate the value of 𝑦 when 𝑥 is equal to three.
Quadratic regression is the process of finding the equation of a parabola that best fits a set of data. In this question, we’re told that the equation is 𝑦 is equal to negative 𝑥 squared plus 5.2𝑥 minus 2.1. We’re asked to calculate the value of 𝑦 when 𝑥 is equal to three. This involves substituting 𝑥 equals three into our equation.
This means that 𝑦 is equal to negative three squared plus 5.2 multiplied by three minus 2.1. Three squared is equal to nine. So our first term becomes negative nine. 5.2 multiplied by three is equal to 15.6. The equation simplifies to 𝑦 is equal to negative nine plus 15.6 minus 2.1. This is equal to 4.5.
The value of 𝑦 when 𝑥 is equal to three is 4.5.