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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how can i put this equation in function of $B$: $A + \sqrt{A^2 + const} = B$

$A + \sqrt{A^2 + const} = B$ Can somebody put this equation in function of $B$. Something like: $A = B \times something$ thank you all :D
Miguel Silvestre
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Quadratic relations

The x intercepts of a quadratic relation are 0 and 5. The second differences are positive. Explain whether the optimum value is a maximum or a minimum Thank for your help because i don't know how the differences are related to the optimum…
sundialdreams
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Why do you have to set the LHS of a quadratic equation equal to zero to solve it?

For example $5=x^2-4x+9$ , set this equation to zero by subtracting $5$ from each side. Why do we have to set it equal to zero to work it out?
Bahar
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Calculating the equation of a parabola by its coordinates

There is some math problems that I can't sort out. The task is that I have N numbers of coordinates (x;y) given that they fit on a parabola and with them, I have to calculate the (ax^2+bx-c) equation of the parabola. I could only make it with 3…
introvertbustardxd
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Formation of quadratic equation using roots

If $a$ and $b$ are the roots of the equation $x^2-px+q=0$, then find the quadratic equation the roots of which are $(a^2-b^2)(a^3-b^3)$ and $a^3b^2+a^2b^3$. My Try So I tried to write the roots in the form of sum and products of roots of the given…
Tanuj
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Simple Quadratic function

If we say that the minimum of a quadratic function is -3 And the sum of its zeros/roots is 2 And I want to find the value of F(1) How do I write down the given here in a more applicable form to the question?
JKM
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Reversing an equation for a sales manager

I need to make a guide for a sales manager letting him know what the lowest he is allowed to sell a product for based on the quantity of the sale. Right now I can only think of a cumbersome equation, as follows: (([sale price]-[cost])-([sale…
Wilf
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If x is a real number, what is the smallest possible value of x sq + 8?

In the solution in the above link, how did they assume x sq to be zero. If x sq is a real no then why couldn't they take is as some -ve number as it is less than 0?
Arpan Panda
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The equation $2x^2-2(2a+1)x+a^2+a=0$ has one root less than $a$ and other root greater than $a$,if

The equation $2x^2-2(2a+1)x+a^2+a=0$ has one root less than $a$ and other root greater than $a$,if $(A)00\hspace{1 cm}(D)a<-1$ As one root is less than $a$ and other root greater than $a$,so…
learner_avid
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How do I solve this quadratic equation in terms of t?

I'm having trouble with this equation. I thought it would be easy to solve using the quadratic formula, but I have no idea how to start. This is not homework, but I would like to know how to solve this in terms of $t$. Both sides are pretty much the…
name
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Sum of all solutions

$$x^2-2(3m-1)x+2m+3=0$$ Find the sum of solutions. It says that the sum equals to $-1$. I just can't wrap my head around this? Any help? Thx
kenobe
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Quadratic equation - change to zero

if you have the following quadratic equation... how do you change 21 to 0?: $x^2 – xy + y^2 = 21$ as far as i know i always have to change it to 0 if it isn't 0. if so; do I add -21 after $y^2$ or add it to $y^ 2$ > $-21y^2$
Feelsbadman
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Quadratic Equation ( x and y ) formula

There's a formula for solving a Quadratic Equation that has $x$ as a variable; e.g: $$2x^2 + 5x - 8x = 0$$ Step 1 (is to find delta/discriminant): $\Delta = b^2 - 4ac$ Step 2 (is to find $x_1$ and $x_2$): $x$ = $\dfrac{-(b) \pm \sqrt\Delta}{2a}$ My…
Feelsbadman
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Please help to find the solution

$$2^{x-2} + 2^{3-x} = 3$$ Please find the value of $x$ and give the solution process.
user456577
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Proof involving quadratic equations

Question: If one root of the equation $ax^2+bx+c=0$ is the cube of the other, prove that, $(b^2-2ca)^2=ca(c+a)^2$. My attempt: To figure out what to do, i did some reverse working. We have to prove that $(b^2-2ca)^2=ca(c+a)^2$ $b^4+4c^2a^2-4b^2ca=…
MrAP
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