# 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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### Vertex form for inverse equations

I was wondering how to use interpret an inverse equation into vertex form, or y=a(x-h)+k So I have this problem: Problem and I used 1/4c and found the vertex (1/2,0) to determine that a = 1/14 and h ...
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### Find the centroid$y = X^2 y= X^2$ [on hold]

Do you guy's know how to solve the question: Find the centroid $y = X^2 y= X^2$ I get the first bit of drawing the axis and the answer to the first step when you find the algebra is 2. Just all the ...
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### $x\in\overline{F}$ is in $F(\sqrt{F})$ $\iff$ $F\subset F(x)$ is finite Galois extension with Gal$(F(x)/F)$ abelian of exponent $2$

Let $F$ be a field of characteristic that is not $2$. I want to prove that $x\in\overline{F}$ is in $F(\sqrt{F})$ $\iff$ $F\subset F(x)$ is a finite Galois extension for which the group ...
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### Second Order Accurate Interpolation

On a grid I am having the values of a physical quantity say for example Temperature, at the E,W,N,S and P node all of them being calculated using a second order discretization scheme. I want a second ...
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### quadratic equation form maximum solutions

My Pearson intermediate algebra book has a "concept check" question in its section on solving equations by using quadratic methods. These questions are supposed to highlight fundamental concepts that ...
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### How to find the range of values of a constant for all values of $x$ [closed]

Question - find range of $c$ for all values of $x$ $$3x^2 - 9x + c\gt 2.25$$ What I don't know is the inequality sign to use in $b^2 - 4ac$
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### Suppose that a function $f(x)=ax^2+bx+c$, where $a,b,c$ are real constants, satisfy the relation..

Suppose that a function $f(x)=ax^2+bx+c$, where $a,b,c$ are real constants, satisfy the relation $$-1\leq f(x)\leq 1$$ for all $-1\leq x\leq 1$, then the maximum value of $f'(x)$ is I think ...
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### Optimization: maximum area of a triangle under a parabola

Optimization: maximum area of a triangle in a parabola Inside a curve ($x^2-25$ - Parabola) a triangle is drawn with A as the vertex at the origin and the line joining points B and C lie on the ...
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### Complex roots of quartic polynomial

This is a question from an undergraduate course on Galois theory: Find all complex numbers which are roots of $P(T)=T^4+2T^2-\sqrt{6}T+\frac{3}{4}$ Can we use Galois theory to solves this? Or ...
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### Solve without using quadratic formula: $\frac{4}{3x+3} = \frac{12}{x^2 - 1}$. [closed]

Solve without using quadratic formula: $\frac{4}{3x+3} = \frac{12}{x^2 - 1}$. Is there a way to solve this without using the quadratic formula? The quadratic formula is one of my biggest weaknesses, ...
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### Solving exponential equation (quadratic type)

I fail trying to solve the following equation: $9^x-6^x-2^{2x+1}=0$ Trying to write it as a quadratic equation makes my constant term exponential $(3^x)^2-2^x3^x-2^{2x+1}=0$ How can I solve this ...
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### $abc$-formula: $D >= 0$ or $D > 0$?

I don't really understand when to put $>$ or $<$ , $>=$ or $<=$ when working with the $abc$-formula. This is the $abc$-formula: We have a quadratic equation: $$ax^2+bx+c$$ Now for the ...
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### Finding the equation of a quadratic with 2 points and a known slope. (SPLINES)

Sketch the spline of degree 2 with value 0.5 at x = 2.5 and the values 1, 1, 0, 0 at t0, . . . , t3, respectively. (t0=0, t1=2, t2=3, and t3=5) What is the value of the spline at x = 1 and 4? What I ...
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### How to represent a system of quadratic equations in matrix form

Suppose I have two quadratic equation like the following: $2x^2 - 3x + 2$ $x^2 + 5x + 6$ I want to find the minimum values of these equation with the constraint that: $-3 \lt x \lt 5$ How ...
### If the quadratic equation $x^2+(2-\tan\theta)x-(1+\tan\theta)=0$ has two integral roots,
If the quadratic equation $x^2+(2-\tan\theta)x-(1+\tan\theta)=0$ has two integral roots,then find the sum of all possible values of $\theta$ in interval $(0,2\pi).$ The given quadratic equation is ...