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How does the discriminant help to identify the solutions to a parabola?
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What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
What is the discriminant and how does it help in knowing how many solutions a quadratic equations will have?
Put the equation into ax²+bx+c=0 form. The discriminant is b²-4ac. If it is negative, there are no real roots. If it is 0, there is one real root. If it is positive, there are 2 real roots. ■
Does a downwards parabola have a maximum?
A parabola that opens downwards has a maximum at its vertex. One way to find it is to take the derivative of the parabola's equation (for y = x2, for example, this is y = 2x), set that to zero, and solve (2x = 0; x = 0). This works because the only horizontal tangent line of a parabola is at its vertex. Please note that WikiAnswers is not here to do your homework for you. If this question is from work you have been assigned by a teacher or professor, I suggest you do the work yourself instead, which will help to increase your understanding of the subject matter and help you to become more familiar with it.
How do you sketch graphs and write equations for parabolas?
If you want to sketch graphs you have to observe the parabola first then find the vertex afterwards you connect them and you've arrived at your answer. In order to write equations for parabolas it has to have x square in it. The standard equation for a parabola is (y - k)2 = 4a(x - h) where h and k are the x- and y-coordinates of the vertex of the parabola and 'a' is a non zero real number. This website at the related link should help, for the equation at least. A parabola is a basic U shaped graph that meets at one point called a vertex. The equation for Andy parabola must have a number being squared such as x2.
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What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
What is the discriminant and how does it help in knowing how many solutions a quadratic equations will have?
Put the equation into ax²+bx+c=0 form. The discriminant is b²-4ac. If it is negative, there are no real roots. If it is 0, there is one real root. If it is positive, there are 2 real roots. ■
How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
How many foci does a parabola have?
A parabola has a single focus point. There is a line running perpendicular to the axis of symmetry of the parabola called the directrix. A line running from the focus to a point on the parabola is going to have the same distance as from the point on the parabola to the closest point of the directrix. In theory you could look at a parabola as being an ellipse with one focus at infinity, but that really doesn't help any. ■
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Does a downwards parabola have a maximum?
A parabola that opens downwards has a maximum at its vertex. One way to find it is to take the derivative of the parabola's equation (for y = x2, for example, this is y = 2x), set that to zero, and solve (2x = 0; x = 0). This works because the only horizontal tangent line of a parabola is at its vertex. Please note that WikiAnswers is not here to do your homework for you. If this question is from work you have been assigned by a teacher or professor, I suggest you do the work yourself instead, which will help to increase your understanding of the subject matter and help you to become more familiar with it.
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