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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Advantages and Disadvantages of the different forms of a quadratic function

My question is when sketching a graph what are the advantages and disadvantages for the following: i. Standard form ii. Factorised form iii. Vertex form Many thanks!
Rawnaa F
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Is a root the input or the solution for the quadratic formula?

For the quadratic formula, what is a root - is it the numbers you put into it (a, b or c) or is it the answers you get after crunching the numbers (x1, x2)?
user9404879
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Conditions for a quadratic equation to be positive?

I was solving a problem in physics when I encountered this problem. I wanted to find the condition where the value of a quadratic equation is positive. Suppose the function is : $f(x) = Ax^2+Bx+C$ Then, I need to find the condition for which the…
therealyubraj
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Quadratic equation -

I have been struggling with this quadratic equation question quite a bit. Specify the zero points for the following function and the coordinates of the parabol peak. $$g(x)=4x^2 +36$$ Edit 1 - this is where I got stuck: $$g(x)=4(x^2+9)$$
James Leaf
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Graph of a parabola

The equation of the following graph is $-x^2-4x-c=y$ how to find c if 3OB=AO
Marva Jami
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Parabola graph problem

Find the maximum vertical distance between parabola and the line Actual answer is 6.25 But why we can't just count it from graph but it give us 6
Marva Jami
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Quadratic function

Find the value of $p$ for which $px^2+4x+p$ is greater than zero for all real value of $x$. I know that if the value of $p$ is $(-\infty,-2)$ and $(2,+\infty)$ the quadratic equation is equal to zero for all real value of $x$ then for which value…
Marva Jami
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Example 1.30 from Introduction to Mathematical Thinking by John D'Angelo

I understand the example. However, I am curious how the author knows to start the argument with $$(1-\lvert x\rvert)^2\ge0.$$ What algorithm does he follow that begins with this assumption?
Bernalillo
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How to solve sum of quadratics

For which integers $n$ does $$(t-n)^2+(t-(n-1))^2+(t-(n-2))^2+...+(t-1)^2=\sum_{i=1}^ni$$ have solutions? I have managed to find an answer to this, but it is probably wrong (example later). Note that this is not a textbook question; rather one…
ə̷̶̸͇̘̜́̍͗̂̄︣͟
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Solving a quadratic equation with square root constants.

I have been struggling on this equation at school, and I seem to find no possible way to do this. Can anyone provide a simple way to find the rules of this equation? $$x + 3\sqrt{x} - 10 = 0$$
Walter Morazan
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Quadratic Equations and their roots.

I want to know if there is any way of finding out whether a quadratic equation has ratonal roots or not.
user168942
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Quаdratic Inequalities

Find the range of values of m for which the straight line $y+mx=12$ intersects the curve $x^2+xy=12$ at two distinct points. I am able to get that $m<4$, but according to the answer key, it should be $m<4, m\neq 1$. I do not understand why $m=1$ is…
Russell Ng
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Determine parameter m so equation has complex results for x:$(m+1)x^2+2(m-1)x+4m+1=0$

$$(m+1)x^2+2(m-1)x+4m+1=0$$ So for results to be complex $b^2-4ac<0$ I then get to a part where I don't know what to do next: $-8m^2-28m<0$. How do I solve m?
RiktasMath
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Solve equation for x: $m^2(z^2-25)=n^2(z^2-25)$

$$m^2(z^2-25)=n^2(z^2-25)$$ I don't get it? I don't even have x anywhere in this equation. Can somebody make this a bit clearer?
RiktasMath
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Question related to a proof in Quadratic equations

If the roots of the equation $a\left(b - c\right)x^{2} + b\left(c - a\right)x + c\left(a - b\right) = 0$ are equal then prove that $2/b = 1/a + 1/c$, i.e. $a,b,c$ are on H.P. I have tried to prove this using the quadratic formula and also with the…
Arunabh
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