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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Given two different quadratic equations in x and y separately, find an ordered pair which satisfies an eqation containing their products.

Let $P(x) = 4(x)^2 +6x+4$ and $Q(x)= 4(y)^2 - 12y +25$ Find the unique ordered pair of real numbers $(x,y)$ that satisfies $P(x).Q(x) = 28$ Please tell me how to answer such questions
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Solving $ x^2-8x+15=0$?

$x^2-8x+15=0$ I always had problems with equations. I tried solving it but I got weird numbers .. I would really appreciate some help and tips how to solve this
Alisia Dogan
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The straight line $y=tx-2$ is a tangent to the graph of a curve $y=2x^2 +4x$, find the value of $t$ ($t>0$)

The straight line $y=tx-2$ is a tangent to the graph of a curve $y=2x^2 +4x$. Find the value of $t$ ($t>0$)
bryan
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2 answers

How to prove that the roots of $(m-2)x^2-(3m-2)x+2m=0$ are real

I need help proving that the roots of the equation: $(m-2)x^2-(3m-2)x+2m=0$ are real. Could you also give me a step by step runthrough of how to do this equation? (I have a few others like this one to do)
Eidolon
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2 answers

How to complete the square for this?

How to express $2x^2 - 3x$ in the form $a(x+b)^2 + c$ where $a$, $b$ and $c$ are constants?
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