In the regression equation, Year 18 is the best prediction for when 2528 people will attend graduate school.
What is the quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of: ax² + bx + c = 0.
The number of people attending graduate school at a university may be modeled by the quadratic regression equation y = 10x2 - 40x+8, where x represents the year.
The regression equation, which year is the best prediction for when 2528 people will attend graduate school is;
[tex]\rm y = 10x^2 - 40x+8\\\\2528 = 10x^2 - 40x+8\\\\ 10x^2 - 40x+8\\\\ 10x^2 - 40x+8-2528=0 \\\\ 10x^2 - 40x-2520=0\\\\\text{Divide by 10 both sides}\\\\x^2-4x-252=0\\\\x^2-18x+14x-252=0\\\\x(x-18)+14(x-18)=0\\\\(x-18)(x+14)=0\\\\x-18=0, \ x=18\\\\x+14=0, \ x=-14[/tex]
Hence, the regression equation, Year 18 is the best prediction for when 2528 people will attend graduate school.
Learn more about quadratic equations here;
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