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 $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

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Solve system with different variables

I need to solve the system: $$x^2+2xy+y^2-1 = 0$$ where variable is $x$ AND $$x^2 + 2xy = 0$$ where variable is $y$. From the first Ι take discriminant, and end in one solution $x_1 = 1-y$ and another $x_2 = -1-y$. I am a little confused on the…
darkchampionz
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Quadratic equation $9x^2-37=6x$ using the quadratic formula

Quadratic equation using the quadratic formula $9x^2-37=6x$ So $9x^2-6x-37=0$ $A= 9$ $b=-6$ $c=37$ $\dfrac{-(-6) \pm \sqrt{ (-6)^2- 4(9)(37)}}{2(9)}$, $\dfrac{6 \pm \sqrt{36-1332}}{18}$, $\dfrac{6 \pm \sqrt {1296}}{18}$ Kindly check if this is…
AlexanderJ
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Solving Quadratic equation by factorizing

The question is 2x^2 - 7x + 3 = 0. First of all quadratic equation is written in the form of ax^2 + bx + c = 0 in where a,b and c are numbers. In this equation I was told to use the matrix method. Since this equation doesnt have a common factor, I…
lase
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Find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$

I'm trying to find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$ can take any real value. These are the steps I've taken so far: $$ xy + ky - x^2 - 3x = 0 $$ Which gives us $a=-1$, $b=(y-3)$, $c=yk$. Using…
hohner
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expanding and simplifying an expression

so the question is $(2x - 2)^2 + (3 - 2x)^2$. My working out: $$ 2x (3 - 2x)^2 + 2 (3 - 2x)^2 = 6x^2 - 4x + 6 - 4x = 2x^2 - 4x + 6. $$ I was a bit confused as their was another way to work out this question which is expanding and simplifying the…
lase
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Expand and simplify

I've removed the brackets from the first equation in where it is 5a^2 + 2a - 5 and then multiplied 3 to the numbers inside the bracket. But I'm not sure what steps to take after that. (5a^2 + 2a - 5) + 3(2a + 2 - 2b^2)
lase
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After completing the square.

After completing the square, what are the solutions to the quadratic equation below? $$x^2 + 2x = 25$$ Honstely I think it's B. But I'm not sure.
user178978
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Quadratic Formula: Sporting Goods World Problem

** A sporting goods store sells 90 ski jackets in a season for $275 each. Each $15 decrease in the price results in five more jackets being sold. What is the lowest price that would produce revenues of at least $19 600? How many jackets would be…
Dev
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Quadratic equations word problem.

A uniform walkway is built around a rectangular flower bed that is 20m by 40m. There is enough material to make a walkway that has a total area of 700 m^2. What is the width of the walkway? I need help making the quadratic equation, the rest I…
Dev
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Can you simplify a coordinate

Can you simplify $(-6,-36)$ to $(-1,-6)$ if the first coordinate is the min value of a quadratic graph. The equation is $y = x^2 + 12x$.
Whos Dench
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Quadratic Function: X intercepts.

A quadratic function with a y-intercept of 0 and an axis of symmetry of x=-1. Apparently, there is suppose to be 2 x-intercepts, which I really don't understand. How can the parabola cross the x axis twice when it has a y intercept of 0? Thanks to…
Dev
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Quadratic Functions word problem.

I have the quadratic function $$y=\frac{1}{294}(x-84)^2-24$$ that represents the shape of the cables of a certain bridge. I am suppose to be determining the vertical height of the cables above the minimum at a point that is $35$m horizontally from…
Dev
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Quadratic Functions Problem

Question: The main section of a certain bridge has cables in the shape of a parabola. Suppose that the points on the tops of the towers where the cables are attached are 168m apart and 24 vertically above the minimum height of the cables. Choose…
user176004
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Equation with the discriminant

I'm stuck on my maths homework, and would appreciate help. The question is: Show that if the equation $(m + n)x^2 - 2mnx - (m-n) = 0$ has equal roots, then $$m^2 = \frac{n^2}{1-n^2}$$ I've worked out that I need to use the discriminant to prove…
imulsion
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Problem involving a quadratic

This is the equation : $mx^2-(4m-1)x+3m-2=0 $ We are asked to find a relationship between the roots that doesn't involve the 'm' parameter. Therefore, I thought the key to achieving this was making use of Vieta's formulas, but nothing useful came…
Victor
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