# Tagged Questions

Questions on quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

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### Why can ALL quadratic equations be solved by the quadratic formula?

In algebra, all quadratic problems can be solved by using the quadratic formula. I read a couple of books, and they told me only HOW and WHEN to use this formula, but they don't tell me WHY I can use ...
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### How to factor $9x^2-80x-9$? [on hold]

How do I factor a trinomial like this? I'm having a lot of difficulty. How do I deal with the $9x^2$?
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### Factoring Quadratics: Asterisk Method

I'm teaching my students about factoring quadratics. We've done GCF, difference of two squares, squared binomials, and grouping. One of my colleagues then found this asterisk method on line. It's ...
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### How to factor quadratic $ax^2+bx+c$?

How do I shorten this? How do I have to think? $$x^2 + x - 2$$ The answer is $$(x+2)(x-1)$$ I don't know how to get to the answer systematically. Could someone explain? Does anyone have a link to ...
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### How to “Re-write completing the square”: $x^2+x+1$

The exercise asks to "Re-write completing the square": $$x^2+x+1$$ The answer is: $$(x+\frac{1}{2})^2+\frac{3}{4}$$ I don't even understand what it means with "Re-write completing the square".. ...
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Is there a method to find which numbers to use when simplifying quadratics? For example $x^2 + 5x + 6$ is easy enough to find, but what if I have bigger numbers, or I have this quadratic expression: ...
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### How do you factor a quadratic expression, without using the formula?

I am asked to factor $2x^2 -3x+1=0$ using factorization, but I run into fractions, and it becomes very messy and complicated to deal with, especially since specifically asked not to use the formula. ...
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### How to solve $\ x^2-19\lfloor x\rfloor+88=0$

I have no clue on how to solve this. If you guys have, please show me your solution as well. $$\ x^2-19\lfloor x\rfloor+88=0$$
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### Derivation of the quadratic equation

So everyone knows that when $ax^2+bx+c=0$,$$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$$ But why does it equal this? I learned this in maths not 2 weeks ago and it makes no sense to me
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### Soft Question: Weblinks to pages with explanation on quadratics.

I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of ...
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### Factor $6x^2​ −7x−5=0$

I'm trying to factor $$6x^2​ −7x−5=0$$ but I have no clue about how to do it. I would be able to factor this: $$x^2-14x+40=0$$ $$a+b=-14$$ $$ab=40$$ But $6x^2​ −7x−5=0$ looks like it's not ...
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### Missing solution in quadratic equation

This is a reformulation of this question to better fit this forum. I removed the mentioning of sage math and this question is now 100% math. Given, the following quadrilateral: I want to describe ...
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### Integrating $\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x$

I've been trying to integrate this: $$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$$ Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up ...
### If $9^{x+1} + (t^2 - 4t - 2)3^x + 1 > 0$, then what values can $t$ take?
If $9^{x+1} + (t^2 - 4t - 2)3^x + 1 > 0$, then what values can $t$ take? This is what I have done: Let $y = 3^x$ $$9^{x+1} + (t^2 - 4t - 2)3^x + 1 > 0$$ \implies9y^2 + (t^2 - 4t - 2)y + 1 &...
### For what real values of $a$ does the range of $f(x)$ contains the interval $[0,1]$?
Question : For what real values of $a$ does the range of $f(x) = \cfrac{x+1}{a+x^2}$ contains the interval $[0,1]$? My doubt lies in the further preceding of this question. The book states : ...