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I'm assuming you are talking about this equation:
x = [ -b +|- sqrt ( b2 - 4ac ) ] / ( 2a )
where, ax^2 + bx + c = 0
The formula is called the quadratic formula. It is used when either factoring is too difficult/tedious or for complex numbers.
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∙ 11y ago
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Why is the equation of the line of symmetry x equals negative b over 2a?
The question refers to the equation of a parabola, that is, a quadratic equation of the form y = ax2 + bx + c. Suppose x1 = -b/2a - z and x2 = -b/2a + z for some real number z. Then y1 = a*(-b/2a - z)2 + b*(-b/2a - z) + c = b2/4a + bz + az2 - b2/2a - bz + c = b2/4a + az2 - b2/2a + c and y2 = (-b/2a + z)2 + b*(-b/2a + z) + c = b2/4a - bz + az2 - b2/2a + bz + c = b2/4a + az2 - b2/2a + c So y1 = y2 thus, if x is the same distance (z) either side of -b/2a, then the corresponding y values are the same. And that, is what a line of symmetry means.
What is 2a equals b?
2a = b Is an example of an equation with linear dependence between the variable a and b (b is twice a)If you know any a you can find the bIf you graph this equation with a on one axis and b on the other (perpendicular) you will get a straight line
What is the quadraic formula?
-b + or - the square root of b squared - 4ac over/divided by 2a
A 2b a b 2a b 2a?
a-^2a-b^-a-b
How do you get from ax2 bx c to the quadratic formula?
ax2+bx+c=0 Multiply the whole equation by 4a: 4a2x2+4abx+4ac=0 Move the 4ac to the other side: 4a2b2+4abx=-4ac Add b2 to both sides: 4a2b2+4abx+b2=b2-4ac The left side of the equation is like (a+b)2=a2+2ab+b2, with a being 2ab and b being b: (2ax+b)2=b2-4ac Do a square root on both sides of the equation: 2ax+b=√(b2-4ac) Move the b to the other side of the equation: 2ax=-b±√(b2-4ac) Leave only x on the left side of the equation by dividing the right side by 2a: x=(-b±√(b2-4ac))/2a The previous explanation: aX2+bx+c is the same as x=-b (plus or minus the square root) of b2 - 4ac divided by two times a. x=(-b±√(b^2-4ac))/2a x can equal (-b+√(b^2-4ac))/2a ∆ (not delta) (-b-√(b^2-4ac))/2a
Examples for quadric equation?
The quadric equation is: negative b plus or minus the square root of b squared minus 4ac all over(divided by) 2a
What is the equation for the axis of symmetry of a parabola?
x=-b/2a [negative B over 2A]
What are some examples of how to use the quadratic formula?
For a quadratic equation in the form: ax² + bx + c = 0 The quadratic formula comes from completing the square of the quadratic equation that gives you a result of x=-b±√b²-4ac divided by 2a. Using a simple quadratic equation like x² + 2x + 1 = 0 a=1; b=2; c=1 x=-2±√2²-4(1)(1) divided by 2a x=-2±√4-4 divided by 2a (4 - 4 = 0 and the square root of 0 is 0) Therefore, x=-2
What is 2a - 7b divided by 3 equals 9?
Since this is a linear equation with 2 variables, it is an unsolvable equation as a and b could be anything, to find an exact answer you need another equation that relates to the first one.
Why is the equation of the line of symmetry x equals negative b over 2a?
The question refers to the equation of a parabola, that is, a quadratic equation of the form y = ax2 + bx + c. Suppose x1 = -b/2a - z and x2 = -b/2a + z for some real number z. Then y1 = a*(-b/2a - z)2 + b*(-b/2a - z) + c = b2/4a + bz + az2 - b2/2a - bz + c = b2/4a + az2 - b2/2a + c and y2 = (-b/2a + z)2 + b*(-b/2a + z) + c = b2/4a - bz + az2 - b2/2a + bz + c = b2/4a + az2 - b2/2a + c So y1 = y2 thus, if x is the same distance (z) either side of -b/2a, then the corresponding y values are the same. And that, is what a line of symmetry means.
How do you solve quadratic equation by competing the square which is not a perfect square?
let, equation is ax2+bx+c=0 so, its solution will be x= (-b-sqrt(b*b-4ac))/2a x= (-b+sqrt(b*b-4ac))/2a it is generalized equation for finding roots of Quadratic eq.
What is the equation of the axis of symmetry of the graph of the equation YXX-5X 6?
X=-b/2a
What is 2a equals b?
2a = b Is an example of an equation with linear dependence between the variable a and b (b is twice a)If you know any a you can find the bIf you graph this equation with a on one axis and b on the other (perpendicular) you will get a straight line
What is the general equation for quadratics?
The general quadratic equation is ax2 + bx + c = 0 The two solutions are: x = [ (negative b) plus or minus the square root of (b2 - 4ac) ] all divided by (2a).
What is a quadratic equation?
A quadratic equation is an equation where a quadratic polynomial is equal to zero. It can be written as ax^2+bx+c=0 where a,b,c are the coefficients and x is the variable. A quadratic equation has always two complex solutions for x given by the formula x=-b/2a+sqrt(b^2-4ac)/2a and x=-b/2a-sqrt(b^2-4ac)/2a. Examples of quadratic equations are x^2+x-2=0, 5x^2+6x=0, x^2+1=0 etc.
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).
How do you find the roots of an equation?
for an 2nd order the roots are : [-b+-sqrt(b^2-4ac)]/2a
