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
3
votes
2 answers

Find quadratic equation given two points and y-intersection

Let the domain be $x \in [0,h]$. We have three points, $(0,1)$, $(h/2,0)$ and $(h,0)$. How do I find the quadratic equation? My attempt: I know that the roots are located at $x=h/2$ and $x=h$. Thus the equation must be of the form $(x-h/2)(x-h) =…
JoJo
  • 31
3
votes
5 answers

Why does the coefficient tell the way a quadratic parabola "opens"?

I've seen a lot of texts referring to the coefficients and their sign for determining which way a parabola opens up. But is there more than this kind of "thumb rule" to it? That is, how was it proven that for those coefficient ranges, the parabola…
mavavilj
  • 7,270
3
votes
2 answers

What is the meaning of a discriminant graphically?

I know that if $b^2-4ac>0$, then there are real solutions and so on. But for any quadratic function, where is the discriminant present in the plot? For example, $x^2-8x+7=f(x)$. Now how is $\Delta=36$ associated with the graph?
Aditya Agarwal
  • 4,595
3
votes
2 answers

Solve in $\mathbb{Q}$ the equation $x^2-(\sqrt{2}+1)x+\sqrt{2}=0$.

Solve in $\mathbb{Q}$ the equation $x^2-(\sqrt{2}+1)x+\sqrt{2}=0$ Somebody can help me? I dont remember how to do.
Let DC
  • 307
3
votes
1 answer

Quadratic equation with greatest integer functioin

$[x]^2-7[x]+12=0$ find $x$? where $[x]$ is Greatest Integer function I have tried to solve the question like this: putting $[x]=y$ , we have the equation: $y^2-7x+12=0$ by solving this equation we get $y=3$ and $y=4$ since $y=[x]$, therefore…
skp777
  • 33
3
votes
1 answer

Is my answer for this quadratic graph question correct?

There is a question in my maths exercises textbook that I have got a different answer than the one given in my textbook. The question is :- For the following graph of the quadratic equation $$ y = ax^2 + bx + c $$ is the product abc is negative? So…
Abhishek Mhatre
  • 691
3
votes
2 answers

How do you solve this quadratic equation?

The number of values of a for which $$ (a^2 - 3a + 2)x^2 + (a^2-5a + 6)x + a^2-4 = 0$$ is an identity in x is? Here's how much I was able to solve through:- $$ (a^2 - 3a + 2)x^2 + (a^2-5a + 6)x + a^2-4 = 0$$ $$ ((a-1)(a-2))x^2 + ((a-3)(a-2))x +…
Abhishek Mhatre
  • 691
3
votes
1 answer

Difference and Quotient of roots of a quadratic equation

In school we are taught the sum and product of roots of $y= ax^2+bx+c$. But are not the difference and quotient of roots equally important? $$x_{1}-x_{2} = \dfrac{\sqrt{b^2-4ac}}{a}$$ $$ \frac{x_{1}}{x_{2}} = \dfrac{b(b+\sqrt{b^2-4 ac})}{2 ac}…
Narasimham
  • 40,495
3
votes
3 answers

Does $2^2=4$ imply $2=\pm \sqrt{4}$?

I read the square root property from the book, College Algebra by Raymond A Barnett and Micheal R Ziegler that, The square root property says, If $A^2=C$ then $A=\pm \sqrt{C}$ I took the equality, $2^2=4$ $\implies 2=\pm \sqrt{4}$ $\implies 2=\pm…
Sufyan Naeem
  • 2,298
3
votes
3 answers

quadratic formula when a and c are positive?

How can you do the quadratic forumla when a and c are positive? I am in a calc class trying to find when the velocity is 0 with a given quadratic equation. But when a and c are positive you get a negative square root, no? ex) $$a= 4,\quad b= 3,\quad…
Omeed
  • 103
3
votes
2 answers

how to find A in quadratic projectile motion

what would the standard form be for this question? During a drumline performance, a drummer throws his drumstick with an upward velocity of 32 feet per second. if the drummer releases and catches the drumstick 6 feet above the ground, what is the…
mark.H
  • 31
3
votes
3 answers

Unfoiling quadratic equation

How can I convert $ax^2 + bx + c = 0$ to a FOIL-style $(x + d)(x - e) = 0$ equation? I have an equation in a computer program that I'm currently solving with the standard $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. If the discriminator is negative I end…
MikeWyatt
  • 131
2
votes
3 answers

Conceptual problem in solving quadratic equation

The sum of all real roots of the equation $$|x-2|^2 + |x-2| - 2 = 0$$ is? I tried this problem by taking two cases $x<2$ and $x>2$ and solving the corresponding equations and I got $8$ as the answer, but in my book the author solves it by taking…
user34304
  • 2,749
2
votes
3 answers

Manipulate the Physics Equation $P = I^2R$ to get R by itself

Given that $P = (V^2 R_1)/(R_1 + R_2)^2$, manipulate the equation so that we get $R_1$ by itself and that we have a quadratic equation. Where $V, P, R_1$, and $R_2$, are variables. I'm stuck when I find that $R_1 = P(R_1 + R_2)^2/(V^2)$
user159778
2
votes
2 answers

Equation with two unknowns

I have this equation to solve and I solved it but don't know if the result is correct. $\begin{cases}2\pi r_1+2\pi r_2=24 & (1) \\ \pi r_1^2+\pi r_2^2=20 & (2)\end{cases}$ Equation $(1)$ gives $r_1=\frac{12-\pi r_2}{\pi}$ Plug that into $(2)$, we…
S4M1R
  • 701
1 2 3
…
64 65