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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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Typical angle in quadratic equations

Typically, when you look at a real world examples for using a quadratic equation/formula, you get a ball being tossed or a missile being launched. I understand what each component of the equation stands for. However, my question is what angle is…
Akara
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How can I pick values for a quadratic formula that are easily solvable?

I am dynamically creating worksheets and I need to come up with some a, b and c values for a quadratic equation that will yield an integer x. How can I do this?
Shamoon
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What is the solution of this quadratic equation problem?

Let $a,b \in \mathbb R$. If for $|x| \le 1$, $|ax^2 + bx + c| \le 1$, find the maximum possible value of $|2ax+b|$ for $x \in [-1,1]$.
jimpix
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quadratic function positive

Put constraints on a quadratic function. I know that for $x > 0$ then $ax^2 + bx + c > 0$ I read around but I just found positive for all $x$. Thanks a lot
john
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Integral values of $m$ for rational roots.

Consider the function $f(x)=mx^2+(2m-1)x+(m-2)$. Choose the correct options: $(A).$ If $f(x)>0$ for all $x \in R$, then $m \in (- \infty, -1/4)$ $(B).$ The number of integral values of $m$ greater than $-5$ so that $f(x)<0$ for all $x \in R$ are…
MathGeek
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For what values of k the expression will be a perfect square?

the question is the expression $kx^2 +(k+1)x +2$ will be a perfect square of a linear polynomial for what values of k . I am unable to understand the concept used in this question for finding the possible values for k. please someone explain.
danny
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Can the two unknowns n and d (in the equations below) be found by using the simultaneous equations method

The two unknowns are n=3 and d=30. So the answers can be easily found by trial and error. Is it possible to find d and n using the simultaneous equation method ? If so could someone do the calculation. I only have schoolboy knowledge and it is two…
Basil Hugh Hall
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how to solve a trignometric quadratic equation?

I am stuck in a question... the questions says $sin^4 x -(k+2)sin^2 x -(k+3)=0$ has a solution then what is the interval in which k must lie. I tried to solve it by putting $sin^2 x =p$ then putting In the equation and then making the discriminant=0…
danny
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What is the equation of the quadratic function through $(2,5)$ with roots $1+\sqrt 5$ and $1-\sqrt 5$?

Determine the equation of the quadratic function that passes through $(2,5)$ if the roots of the corresponding quadratic equation are $1+\sqrt 5$ and $1-\sqrt 5$.
IAmAboutToFailLol
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Vertex (smallest possible value) of $ax^2+bx+c$

The original problem was this: Find the smallest possible value of $ax^2+bx+c$, where a, b, and c are given numbers and $a>0$, and x is some number. I already asked this, and got a decent answer, but let me get this clear; am I correct here? The…
Kurns
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Smallest possible value of $ax^2+bx+c$

The problem goes like this: Let $a, b$ and $c$ be given numbers, where $a>0$, and let $x$ be some number. What is the smallest possible value of $ax^2+bx+c$ ? The terms 'given number' and 'some number' really bother me. Now I'm just really confused…
Kurns
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How to find quadratic vertex form function given a point?

Write an equation of a parabola that has a directx of y= -5 and a focus at (2,-1)? I'm guessing focus here means the vertex $$ Y = a(x-h)^2 + k$$ $$-5 = a(x-2)^2 -1$$ $$-5 + 1 = a(x-2)^2$$ If i take the -4 to the other side than it would be…
MATH ASKER
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Can't find my mistake

I'm trying to find the sum of the reciprocal numbers of squares of quadratic equation:$3x^2-14x+6=0$, I managed to find the answer by calculating the roots, and summing their reciprocal. However firstly I tried to do it using viet's formulas here is…
Planet_Earth
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Equations $ax^2+btx+c=0, bx^2+ctx+a=0$ and $cx^2+atx+b=0$

Find different real numbers $a,b,c,t$ for which the following conditions: 1) the equation $ax^2+btx+c=0$ has real roots $x_1,x_2$; 2) the equation $bx^2+ctx+a=0$ has real roots $x_2,x_3$; 3) the equation $cx^2+atx+b=0$ has real roots $x_1,x_3$,…
Roman83
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finding rational roots

Consider the integral expression in $x$ $$P=x^3+x^2+ax+1,$$ where $a$ is a rational number. At $a= ?$ the value of $P$ is a rational number for any $x$ which satisfies the equation $x^2+2x−2=0$, and in this case the value of $P=?$ I don't know how…
Shira
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