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

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I've come across a problem that results in the equation: $t -2t\sin t -2\cos t -2 = 0$ I've tried to do this analytically but I can't figure it out. At this point, I just want to know if it's even ...
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### If a downwards curve's tangent point is at $(0, -15)$, what is the equation for the tangent line of this curve?

Question is in the title. If a downwards curve's tangent point is at $(0, -15)$. So, what is the equation for the tangent line of this curve? Edit: the equation of the curve is $y = x^2 + 2x - 15$
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### Multiplying by $1$ adds a solution to an equation

I have a question, which is motivated by my book's solution to finding the inverse function of $f(x)=\frac{x}{1-x^2}$ with the domain of $f(x)$ restricted the open interval $(-1,1)$. The questions are ...
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### What's the value of a quadratic function when $x=0$ if the degree of the constant term is $0$? [duplicate]

The degree of the constant term in a quadratic (or any polynomial) is $0$. Say, I have the following quadratic function: $$f(x) = 2x^2 + 4x +7$$ Since the degree of the constant term is $0$, I can ...
I'm trying to show a quadratic equation of the form $$\frac{1}{2} a' \Sigma^{-1} a x^2 - a' \Sigma^{-1} \iota x + \frac{1}{2} \iota' \Sigma^{-1} \iota$$ has a real solution. Here $\Sigma$ is an $N \... 1 vote 1 answer 41 views ### formula for coefficients of Least Squares Regression Quad? According to Maths Is Fun, the formula for coefficients of Least Squares Regression Line is: ... -3 votes 1 answer 46 views ### quadratic expression problem [closed] I was going through my old mock exams I found this question wich I still dont know how to solve. I've done some working out, however I don't really understand the format of the answer sheet plus don't ... 1 vote 1 answer 18 views ### Determining the signs of certain expressions formed by the coefficients of a quadratic (Graph of quadratic given) Consider the quadratic$y=ax^2+bx+c$with the following graph: I'm trying to figure out the sign of the following expressions: 1).$\frac{c}{a}$2).$b+4a$3).$2a+b$The vertex form may prove to be ... 2 votes 0 answers 55 views ### Condition for two quadratic equation to have one common root (Simplification) If a,b,c are in Geometric Progression, then the equations$ax^2+2bx+c=0$and$dx2+2ex+f=0$have a common root if$\frac da, \frac eb, \frac fc$are in: Arithmetic Progression Geometric Progression ... 0 votes 0 answers 49 views ### To find Possible values of combinations of a & b for$a^2 + b^2 = 576$or any quadratic equation under certain restrictions. Q: Find possible values of combination of a&b such that$a^2 + b^2 = 576$or any other quadratic equation under certain restrictions. The sole purpose is to understand how can we do it: CONDITION: ... 2 votes 3 answers 126 views ### Finding the slope of line intersecting the parabola A line$y=mx+c$intersects the parabola$y=x^2$at points$A$and$B$. The line$AB$intersects the$y$-axis at point$P$. If$AP−BP=1$, then find$m^2$. where$m > 0$. so far I know$x^2−mx−c=0,\$ ... 