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 $y=a(x+b)(x+c)$.

5,162 questions
Filter by
Sorted by
Tagged with
41 views

### What will be the value of k for which equation $x^2–4|x|+3=|k−1|$ has four real roots?

The equation is $$x^2–4|x|+3=|k−1|$$ There are several ways to find the solution using either graph or analytically. I want to know is how to do the graphical solution free hand without a calculator. ...
30 views

### Quadratic surface where variables are functions

Is it possible for a quadratic surface to have variables and coefficients that are functions? For example, an equation such as $$A(T)x(T)^2 + B(T)y(T)^2 + C(T)z(T)^2 + D(T)x(T)y(T)\;...$$ where both ...
• 23
78 views

### Why is $f(x)\equiv f(x+2k)\pmod k$ for$f(x)=x(x+1)/2 + c.$

I came across this in a programming contest: f(x)%k = f(x+2k)%k for f(x)=x(x+1)/2 + c I first thought that this is a property of Harmonic numbers only but after ...
• 453
45 views

### Is there a general method for solving a parabola in integers? [duplicate]

A parabolic equation such as the following: $$538445x + 75816 = y^2$$ with general form: $$ax + b = y^2$$ By a brute-force search, one Diophantine solution is $$x = 2312$$ Is there a smarter, ...
• 145
79 views

### How are the domain and range of a quadratic function determined?

How are the domain and range of a quadratic function determined?For example, what are the domain and range of $x^2-4x+10$
• 19
65 views