Hello! My Question is: Find an equation that represents the family of 2nd degree

Question

Hello! My Question is: Find an equation that represents the family of 2nd degreepolynomials that pass through the points (0, 1) and (1, 2) (Hint: The equation will invovle one arbitrary parameterthat produces the memebers of the family when varied) Please list steps!! Thanks for your help!! Hello! My Question is: Find an equation that represents the family of 2nd degreepolynomials that pass through the points (0, 1) and (1, 2) (Hint: The equation will invovle one arbitrary parameterthat produces the memebers of the family when varied) Please list steps!! Thanks for your help!!

Explanation / Answer

The general equation of a 2nd degree polynomial function can bewritten as, y = ax2 + bx + c We need the equation to satisfy both points (0, 1) and (1, 2). Plugging in (0, 1), we get 1 = a (0) + b (0) + c c = 1 So, we're left with y = ax2 + bx + 1 Next, we need it to satisfy (1, 2) 2 = a (1) + b (1) + 1 2 = a + b + 1 b = 1 - a Thus, our general family of functions that pass through (0, 1) and(1, 2) is y = ax2 + (1 - a)x + 1 where the parameter a can be varied.

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