Find four functions of the form f(x)=ax^2+bx+c that would have the same x-interc

Question

Find four functions of the form f(x)=ax^2+bx+c that would have the same x-intercepts as the function f(x)=(1/4)x^2+(2/3)x-(5/6). In each of your four functions, the values of a, b, and c must be integers. Finally, use one ofyour functions (or you can use the given one) to actually find the x-intercepts that each of your functions share with the given one. This must be done algebraically (so, show your work) and the answers need to be exact and simplified completely. Find four functions of the form f(x)=ax^2+bx+c that would have the same x-intercepts as the function f(x)=(1/4)x^2+(2/3)x-(5/6). In each of your four functions, the values of a, b, and c must be integers. Finally, use one ofyour functions (or you can use the given one) to actually find the x-intercepts that each of your functions share with the given one. This must be done algebraically (so, show your work) and the answers need to be exact and simplified completely.

Explanation / Answer

Well if you want a general algorithm to solving this problem, first just use the quadratic formula x = (-b +or- sqrt(b^2-4fac))/2a with your given equation to solve for the x-intercepts. Once you find the zeroes, use the general parabolic equation and set it to 0: ax^2 + bx + c = 0 And then substitute whatever x-intercepts you got from your original equation into "x" for this equation, set 2 variables (out of a, b or c) to a constant, and solve for the remaining one. You'll easily get 4 different functions if you do this :)

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