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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Looking for a familiy of quadratic functions with vertices along a line

I am looking for a familiy of quadratic functions with the following characteristics: the vertex is at y=1 and in the interval [2,4] for x the parabola runs through (0,0) So my "leftmost" function is $-\frac{x^2}{4} +x $ and the "rightmost" one is…
Peter Leupold
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Why do I have to use a quadratic equation?

I don't understand why this doesn't work: Problem: $$x^{2}+x-2=0$$ Solution: $$x^{2}+x=2$$ $$x+x=\sqrt{2}$$ $$2x≈1.4$$ $$x≈1.4/2$$ $$x≈0.7$$ Checking: (Note: I made the calculation with more decimals than the amount I wrote here; that explain…
Ender Look
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Finding the solution of a biquadratic

If $a$, $b$, $c$, $d$ are distinct integers such that $(x-a)(x-b)(x-c)(x-d)=9$ has an integral solution say $h$. Then find the value of $(a+b+c+d)/h$.
user
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Locus & Parabola: find the equation of the parabola

Please explain how to solve this question: Find the equation of the parabola with coordinates of the vertex being $(0,0)$ and equation of the axis $x = 0$, passing through the point $(-1, 7)$. Thanks
Liana Pavlicheva
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Quadratic equation problem involving rectangles

In the centre of a rectangular lawn of dimensions $50 m \times 40 m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184 m^2$ . Find the length and breadth of the pond.
Arunabh
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unification of two quadratic equations with two variables

I have two quadratic equations with two variables like below: $f(x,y)=18xy+5x+19y+5$ $f(x,y)=18xy+11x+7y+4 $ Is there a way to unite the two equations? Are there any SW tools that could render the two equations and as output yield a third…
Salman Farsi
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Roots of bi-quadratic equation

I got an question to find the product of the roots of $x^2 + 18x + 30 = 2\sqrt{x^2 + 18x + 45}$. This is what I did: $y = x^2 + 18x$. So $y + 30 = 2\sqrt{y + 45}$. Squaring it on both sides: $(y + 30)^2 = (2\sqrt{y + 45})^2\Rightarrow y^2 + 30^2…
infixint943
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Finding the value of $k$ when the parabola is tangent to $x$-axis

What is the positive value of k for which the graph is $y=x^2 -2kx+16$ is tangent to the $x$-axis? My approach to solving this is that since the parabola is tangent to the $x$-axis, I can find the value of $x$ by using $-\frac{b}{2a}$. Once I have…
Somebloke
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Quadratic equation that takes 2 zeroes and keeps the vertex at y = 10

I'm not the best at algebra so I will try to word this in the best way I can. Let's say I have 2 solutions in each of 2 solution sets: Set 1: (6, 0) and (18, 0) (visual here) Set 2: (0, 0) and (2, 0) (visual here) As you can see, the y position of…
Encoded Lua
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Maximize Profit from a Quadratic Equation

I've been working with the following word problem: The following equation represents the number of wooden blocks, $b$, that a company can produce per minute using wooden boards, $w$: $$b^2 = \frac{w}{2}-2$$ It costs the company \$1 to purchase each…
Richard Torres
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How to find the range of this expression

I have : $$ \frac{x^2+2x+1}{x^2+2x+7} $$ Where x is real. I need to find out its range. I tried: Let $ \frac{x^2+2x+1}{x^2+2x+7} = y $ Which gives me: $ 24y^2 - 28y + 3 =0 $ And I am confused what to do next.
Maanav Roy
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How to solve this quadratic equation?

Question: Given that $r$ is a root of the quadratic equation $x^2−3x−5=0$, find the value of $2r^2−6r+1$ Thx a lot, because I can't see the pattern of this quadratic equation, so I am struggling a lot to use $r={3±√29\over 2}$ in $2r^2−6r+1$
Katikota
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Why am I not getting the desired result to simplify and derive $y^2 - z^2$?

I completed my high-school maths test and got $96$% which I was very proud of (not meaning to boast). But there was one question which I got $2$ marks on instead of $4$ and didn't know why when I looked back at my results. $\tag{4 marks}$ Question…
Mr Pie
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Solve the quadratic with 4 unknowns

I know how to solve quadratic equations with the quadratic formula but this question has really got me stumped. $$h=-16t^2+vt+s.$$ I am trying to solve for t but I have no idea where to start since there are 4 variables. Could somebody give a step…
C Miller
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How can I simplify this equation? $x\sqrt[3]{x}+4x^{\frac{4}{3}}-5\sqrt[3]{x^4}$

How can I simplify this equation step-by-step? $x\sqrt[3]{x}+4x^{\frac{4}{3}}-5\sqrt[3]{x^4}$ My…
Caio Tarifa
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