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Equations with an order of 2 (contains a value to the power of 2, i.e. x2).
An example of a quadratic equation is:
x2 + 10x + 7
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How do you judge whether an equation has solutions by looking at it in standard form?
If you're talking about two linear equations, make sure they are not parallel. If you're talking about quadratics, make sure that b2-4ac is not negative.
How are quadratic equations used in real life?
Many real life physics problems are parabolic in nature. Parabolas can be shown as a quadratic equation. If you have two variables then usually you can use the equation to find the best solution to a problem. Also, it is a beginning in the world of mathematical optimization. Some equations use more than two variables and require the technique used to solve quadratics to solve them. I just ran an optimization of 128 variables. To understand the parameters I needed to set I had to understand quadratics.
What are the solutions to the quadratic x2-2x-48 equals 0?
X^2 - 2X - 48 = 0 what two factors of - 48 add up to - 2 ? (X + 6)(X - 8) X = - 6 --------- X = 8 ---------by inspection can solve many quadratics
What quadratic function when graphed has x intercept of 4 and 3?
The simplest example that fits that is y = x^2 - 7x + 12. A math professor wouldn't like the process, but assuming we want a positive quadratic, and since positive quadratics are symmetrical along their minimums, we can skip some steps. We know that the local minimum is going to lie exactly between 3 and 4, at x = 7/2. Put everything on one side to get 2x - 7 = 0. Taking the integral (and skipping a few more steps) gets y = x^2 - 7x + c. Solving for c where y = 0 when x = 3, we find c = 12.
What are the pros and cons of solving quadratics by using the quadratic formula?
One pro of using the quadratic formula is that it will produce complex (imaginary) roots just as easily as it can produce real roots. (Factoring with imaginary numbers is a kind of a nightmare!) Another pro to the quadratic formula is that it eliminates the frustrating guess-and-check process. A con of the quadratic formula is that, when it comes to more simple problems, it is usually more time-consuming. A lot of textbook problems are quite easy to factor in your head--it is often not worth the effort of plugging numbers into a long formula. A second con of the quadratic formula is that it is quite long--you might write out the formula, accidentally forget a letter, and whole thing is useless. It's much easier to see that your work is correct when you're factoring.
