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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Determine the equation of a parabola with roots $2 + \sqrt {3}$ and $2 - \sqrt {3}$, and passing through the point $(2,5)$

My attempt: $$f(x) = a(x - r)(x - s)$$ $$f(x) = a(x-(2 + \sqrt {3}))(x-(2- \sqrt {3}))$$ From here, I'm stuck. I can't remember where to go from this point and need some help.
user287997
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No. of parabolas possible for the given equation.

Given, $f(x)=-x^2+qx+r$. $(q,r) \epsilon R$. $q,r$ are variables. A quadratic equation $f(x)=0$ has a maximum value $m$ ($m$ is a constant) and a root $x=a$. Does $f(x)$ correspond to a unique parabola? Why?
Anubhab Das
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Bound on Coefficients

For real $a,b,c$ the following holds $|ax^2+bx+c|\le 1 ; \forall x\in [0,1]$.Show that $|a|+|b|+|c|\le 17$. Cant show that the equality holds.I always get the lesser bounds.
user300191
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Deriving Quadratic Function Using Table of Values

How do you derive a quadratic function given its table of values when there is no zero x value given? For example, x|1|2|3 y|-6|-3|4 I tried two methods in solving this but I can only get a. Any suggestions?
None of YerBiz
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Determining Parabola by Equation Problem

I need some help figuring out how to solve this problem. Which of the following could be a graph of the equation $ y= ax^2 + bx + c$ where $b^2 - 4ac = 0$ The picture below was the correct answer. So the first equation told me that the the shape…
j76goatboy
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Quadratic Equation Application

Textbook exercise I get stuck "Amy is going to hold a concert at a stadium. The stadium can accommodate 12 000 people. If the price for each ticket is \$160, all the tickets will be sold. For every increase of \$1 in the ticket price, the number…
user256670
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Factorising quadratic equation with an unknown given 1 root

In a algebra quadratic question, it says: The equation $3x^2+4x-k=0$ has two distinct real roots. If 2 is a root of this equation, find the value of $k$ and the second root. The first line of working for this question shows as: $(3x+n)(x-2)=0$ The…
Spica
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Quadratic equation involving right-angled triangle

I have right angled triangle I've been attempting to prove a quadratic equation with for a while. It has a hypotenuse of $2x + 1 cm$, a base of $x + 5 cm$, and height of $x - 2 cm$. I calculated its area to be $x^2 + 3x - 10$, but am now confused. I…
GregW
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Solving the following equation by factorisation

The given equation is, $\frac{m}{n}x^2+\frac{n}{m}=1-2x$ What I've tried, Multiplying the equation by $n$, we get $mx^2+\frac{n^2}{m}x=n-2nx$ Now what? I am completely confused about what to do. Have I followed the correct steps?
Abhishekstudent
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Algebraic Solution to $z^2 = az + b^2$

In a book about the history of invisible numbers, the author writes: $\frac 1 2 a + \sqrt {(\frac a 2)^2 + b^2}$ is the solution to $z^2 = az + b^2 $ Where is this coming from? I could not find a way to work it out through the quadratic formula.
Haim
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Sum of equation's roots

Find the sum of all real roots of all polynomials in the form of $y=x^2+px+122$, where $p$ can be all integers in the range $[-35,17]$ I could only do it via excel) Which is not mathematical proof..
nlimits
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Quadratic Equation by Factoring

My son has this problem on his homework and I can't figure out the process to solve this equation. The instructions say "Solve each equation by factoring". Can someone help and please show steps? (7b+1)(7b-5) = 0
Josh DeLong
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Quadratic equation problem

Quadratic eq which takes the value (y) = 41 at x= -2 , the value (y) = 20 at x =5 when x = 2 -> a4-b2+c=y ... how to find a,b,c,y here is original question: Question's pic
Cool
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Intersections of a quadratic equation with the X-axis

Given a quadratic equation $(x)=2x^2 -4kx+3k^2+5$, where $ k$ is a constant. I want to find out if the equation intersects the X-axis by measuring the delta, which is equal to $-8k^2-40$ Then I conclude that there are intersections if $k$ is between…
Corey
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Under which conditions do positive real roots exist in a quadratic of two variables?

Suppose we have a quadratic polynomial equation in two variables: $$p(x,y) = ax^2 + by^2 + cxy + dx + ey + f = 0$$ Under which conditions does at least one solution $p(x,y)=0$ exist with $x$ and $y$ both real and positive?
Jules
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