Why Does the Quadratic Formula Give Unexpected Graph Results?

[Firepanda]

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

 

[Mark44]

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.

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.

 

[Architeuthis Dux]

for your question. The quadratic formula is a useful tool for solving quadratic equations, which are equations in the form of ax2 + bx + c = 0. The formula is given by:

x = (-b ± √(b2-4ac)) / 2a

Where a, b, and c are the coefficients of the quadratic equation. This formula can be used to find the roots, or solutions, of the quadratic equation.

In the case of the equation -x2 - bx + c = 0, we can rewrite it as x2 + bx - c = 0 by multiplying both sides by -1. Now we can see that a = 1, b = b, and c = -c. Plugging these values into the quadratic formula, we get:

x = (-b ± √(b2-4(1)(-c))) / 2(1)

= (-b ± √(b2+4c)) / 2

This is the same as the formula you provided, except for a minor error in the denominator. The correct formula should be (-b ± √(b2+4c)) / 2. So, the roots of the equation -x2 - bx + c = 0 are given by:

x = (-b ± √(b2+4c)) / 2

I'm not sure about the issue you are having with graphing this function. If you are using a graphing calculator, make sure you are entering the formula correctly and using the correct values for a, b, and c. If you are graphing by hand, make sure you are following the correct steps for graphing a quadratic function. I hope this helps clarify things for you.