Why Does the Quadratic Formula Give Unexpected Graph Results?

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SUMMARY

The discussion centers on the application of the quadratic formula to the equation -x² - bx + c = 0. Participants clarify that the correct roots are given by x = (-b ± √(b² + 4c)) / 2, regardless of the sign in front of the x² term. A suggestion is made to multiply the entire equation by -1 to simplify the graphing process, which maintains the integrity of the solutions. The confusion arises from potential sign errors when inputting the equation into graphing utilities.

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  • Familiarity with the quadratic formula and its components.
  • Basic knowledge of graphing functions using graphing utilities.
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Firepanda
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Applying it to

-x2 - bx +c = 0

I would have thought it to be

(b +- (b2+4c)0.5) /-2

= (-b +- (b2+4c)0.5) /2


But

Anytime I try and graph a function like it the roots are

(b +- (b2+4c)0.5) /2

I can't see why this is?

Thanks
 
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Firepanda said:
Applying it to

-x2 - bx +c = 0

I would have thought it to be

(b +- (b2+4c)0.5) /-2

= (-b +- (b2+4c)0.5) /2
Yes, the roots of the equation above are x = (-b +- (b2+4c)0.5) /2.
Firepanda said:
But

Anytime I try and graph a function like it the roots are

(b +- (b2+4c)0.5) /2

I can't see why this is?

Thanks
I can't either, but I suspect you're doing some unconscious sign-changing of the coefficients when you enter the function into whatever graphing utility you're using.

Regarding your first equation, why don't you multiply both sides by -1 to get x^2 + bx - c = 0? The solutions would be the same.
 

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