Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [quadratics]

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

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

The root of $y=ax^2+bx+c$ can be solved by the formula $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

5400 questions
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Solve $\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2$

Solve the equation $$\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2 $$ My reference gives the only solution as $-1$. I can indeed verify this solution but don't have any clue of how to solve for it. I think squaring might a possible but that seems…
Sooraj S
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Finding minimum value of relation with quadratic coefficient

Let $f(x)= ax^2 +bx+c$, such that $f(x)\geq0$. Find minimum value of $\frac{f(1)}{f(0)-f(-1)}.$ My attempt: denominator should be maximum so $f(-1)=0$ as $f(x)$ is always greater than or equal to zero. So I got $b=2a$, $c=a$. But then I am getting…
maveric
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Finding how many intersections two parabolas have within a certain domain

I need to find out if $y=x^2-\sqrt{200}x+50$ and $y=a(x-\sqrt8)^2$ how for what values of $a$ they will have only one point of intersection within the domain $[\sqrt8,\infty)$?
Bobbo
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Solving quadratic equation for inverse variable

I'm reading through some lecture notes and they show a quadratic equation, which I will just write in the usual way as $$ax^2+bx+c=0$$ The notes say that, even though that equation can be solved in the usual fashion, it's easier to solve the…
Dirac
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Calculate quadratic function from given points in 2 dimensions

The quadratic function can be defined as $z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$ But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$? I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to…
user32038
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Determining whether a quadratic has a maximum or minimum

So I've learnt that quadratics equations with a positive coefficient on the squared term have a minimum and a maximum if the coefficient is negative. But if we rearrange the quadratic and change the signs of the squared term, doesn't that mean the…
user552217
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Change the vertex of a parabola while ensuring it still passes through a particular point

I have a parabola defined by the quadratic equation $y = -(x + 0)(x - endPoint)$, which also passes through a particular point $(a, b)$. I would like to know how to alter the equation so that I can ensure that the vertex of the parabola reaches a…
ashaquick
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The quadratic function problem

$H(p,q)$ and $I(r,s)$ are two points on $f(x)=x^2-6x+11$. If $p+q=6$, what is the relationship between $q$ and $s$?
Asri Hazwan
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Generating function with multiple variables with perfect square

Consider trinomial $x^2 + bx + c = 0$. When $b = 205$ and $c = -206$, then $x = 1$ and the function evaluates to a perfect square. My question is, how can I choose $b$ and $c$ and generate functions that are always a perfect square? I tried trial…
michael501
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$3x^2+5xy-2y^2-3x+8y+\lambda$ How to express as two factors

$3x^2+5xy-2y^2-3x+8y+\lambda$ find appropriate value for $\lambda$ such that expression can be expressed as two linear factors. My Try First I thought of separately writing x terms as complete squares and y terms as complete squares, then…
emil
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How to properly write a solutions of quadratic equation on one line?

Using this formula $$x_{1,2}={-b\pm\sqrt{b^2-4ac} \over 2a} = \space \cdots$$ what should be the correct format of the solution if I want to put both roots (x) on one line? Thanks in advance
user635053
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Calculate protein concentration (x) from known absorbance

Got known absorbance ($y$) and I want to find $x$ from this formula: $$y = -4\times 10^{-7} x^2 + 0.001 x + 0.2529$$
Cibic
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Minimum possible number of positive root of the quadratic equation $x^2-(1+\lambda)x+\lambda-2=0,\lambda\in R$ is

Minimum possible number of positive root of the quadratic equation $x^2-(1+\lambda)x+\lambda-2=0,\lambda\in R$ is $(a)2$ $(b)1$ $(c)0$ $(d)3$ $x^2-(1+\lambda)x+\lambda-2=0$ I changed this equation to $\lambda=\frac{x^2-x-2}{x-1}$.I am stuck now.
user984325
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The greatest area for a rectangle on a track field.

An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the greatest possible area for the rectangular region. This is the work that I did below. I was…
mjj
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