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How does the formula -b over 2a work?

Updated: 4/28/2022
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Legendofhonor5

Lvl 1
13y ago

Best Answer

The quadratic formula is "[minus b] over 2a, plus or minus the square root of [b squared minus 4ac], over 2a".

where the formula for the variable is in the form

a(x2) + b(x) + c = 0

By setting the equation into this form, you can use the integer values a, b, and c to find the solution for x, simply by multiplying, taking the square root, and adding. As the equation describes a curve, the two solutions (plus or minus) are the x-intercepts (y=0) of the curve, and the y-intercept (x=0) is at c.

* For the shorter form ax2 + 2kx + c where k is an even number, see the related link.

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Q: How does the formula -b over 2a work?
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What is the quadraic formula?

-b + or - the square root of b squared - 4ac over/divided by 2a


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The quadratic formula is x=-b (+or-) square root of b2-4ac all over 2a


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x=-b/2a [negative B over 2A]


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How does the formula -b over 2a give the x value of the vertex given ax2 bx c?

From the quadratic formula, the zeros (where y=0) is -b/(2a) +/- sqrt(b^2 -4ac)/(2a). The expression inside the square root is known as the descriminant. Being that the parabola is symmetric, one of the zeros will be at the vertex + sqrt(b^2 -4ac)/(2a) and the other zero is at vertex - sqrt(b^2 -4ac)/(2a). The vertex is halfway between these two values, so the x coordinate of the vertex is -b/(2a). Or if you use Calculus, you can take the derivative of f(x) = ax^2 + bx + c. f'(x) = 2ax + b. Set equal to zero and solve for x. x = -b/(2a).


What is the axis of symmetry formula?

-b/2a. i think.To show this, consider this equation:y = ax² + bx + cFactor out the a:y = a(x² + bx/a + c/a)Then, complete the squares to get:y = a(x² + bx/a + (b/(2a))² + c/a - (b/(2a))²)= a((x + (b/2a))² + c/a - (b/(2a))²)= a(x + (b/2a))² + c - b/(4a)By the vertex form:y = a(x - h)² + k where x = h is the axis of symmetry.So the general axis of symmetry for the quadratic equation is x = -b/(2a).


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Try the quadratic formula. X = -b ± (sqrt(b^2-4ac)/2a)


Where did the quadratic formula come from?

The quadratic formula originated from the concept of completing the square. let's take ax2 + bx + c = 0. To complete the square, solve for x. Subtract c. ax2 + bx = -c. Then divide by a [notice- if there is no a value, then a=1]. x2 + bx/a = -c/a. Add (b/2a)2 to both sides. x2 + bx/a + b2/4a2 = -c/a + b2/4a2 Factor/Reformat. (x + b/2a)2 = (b2-4ac) / 4a2 (x + b/2a)2 = [(b2-4ac) / 2a]2 Square-root both sides. x + b/2a = ± √(b2-4ac) / 2a Subtract b/2a. x = -b/2a ± √(b2-4ac) / 2a Combine terms. x = [-b ± √(b2-4ac)] / 2a


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