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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Finding the vertex of a quadratic function

I'm in the process of relearning math and came across a problem when calculating the vertex for $5x^2-20x+15$ function. I took the following steps to find the vertex: I divided every term by 5 to get a simplified equivalent function $x^2-4x+3$ Put…
Peter
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Creating a quadratic given roots using the principle of zero products

Using the Principle of Zero Products, create a quadratic in standard form that has roots of $-1$ and $\frac{3}{2}$. Values of $a, b$, and $c$ in your final form should all be elements of the set of integers. I really don't understand how to do…
RetroBreads
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Show that the quadratic function $g(x)= 2x^2 - 4kx + k^2$ intersects the $x$-axis for all values of $k$.

Should I use $b^2 - 4ac$? Is the answer $8k^2 > 0$?
phoebe
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Quadratic equation with parameter (what method to use to obtain correct answer)

For which values of the parameter $k$ does the equation $(2k-5)x^2-2(k-1)x+3=0$ have exactly one real answer? From my work I determined $k = 4$, but the answer is $[k=4 \lor k=\frac{5}{2}]$. The symbol $\lor$ I believe is supposed to indicate…
SloppyPuppy
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Transform quadratic to perfect square

If one wanted to transform $y(x) = ax^2 + bx + c$ to the form $(ux + v)^2,$ is there a transformation you can make in terms of $y(\text{subsitution}) = (ux + v)^2$?
PhiEarl
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Quadratic substituted into itself : wrong?

Let $x^2=x+1$, the solution is the golden ratio phi :$x=\frac{1\pm\sqrt{5}}{2}$. Now I tried $x=x^2-1$ substituted in the equation itself : $$(x^2-1)^2=x^2\Rightarrow x^4-3x^2+1=0$$ $$\Rightarrow x=\pm\sqrt{\frac{3\pm\sqrt{5}}{2}}$$ Now we get 4…
QuantumPotatoïd
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Quadratic inequality, Discriminant

The equation of a curve is $y=ax^2+5x+a-5$, where $a$ is a constant. In the case where $a=2$, find the set of values of $x$ for which the curve lies completely above the line $y=9$. I sub $a=2$ and solve using simultaneous equation and get $x=1.5$…
Jayle
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$S$ and $G$ are roots of $x^2 −3x +1=0$. Find equation whose roots are $\frac{1}{S -2}$ and$\frac{1}{G-2}$

If S,G are roots of $x^2 −3x +1=0$, then find equation whose roots are $\frac{1}{S -2}$ , $\frac{1}{G-2}$. So , the way my sir solved it is that He took x = $\frac{1}{S -2}$ , then he got S = $\frac{2x+1}{x}$. I am confused with is that we were told…
user848010
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How to reduce 2 quadratic forms to a canonical form

How to reduce 2 quadratic forms to a canonical form EX: P=$ x^2+y^2+z^2+4xy+4yz+4zx$ and $Q=xy+yz+zx$
ARI
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Find all the real roots of $ x^2 + x^2/(x+1)^2=3 $

Find all the real roots of $x^2 + \frac{x^2}{(x+1)^2}=3$. I got a 4th power equation after simplifying but didn't understand what to do afterwards
will the wise
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Solving an equation with 2 square terms

Consider this equation; $$ 3x^2 + 2dx - d^2 = 0 $$ Now I need to find the value of x.I've consider using the quadratic formula but I've got 2 squared terms. I've also tried forming the equation to get x squared on one side, but than I'm not sure…
codeisfun
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What is the value of p?

Working on a ACT practice problem with my son. In the equation x^2 + px + k = 0, p and k are integers. The only possible value for x is 4. What is the value of p? I think the fact that it says p and k are integers are key to solving this problem, I…
polyhedron
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How to solve this bi-quadratic example?

$$5\left(\frac{x+1}{x}\right)^2 - 16\left( \frac{x-1}{x}\right) - 52 = 0$$ I learned how to use a swap for instance I'd say that $$\frac{x+1}{x}=t$$ and then swap throughout the equation, but I'm stuck here, I can't get rid of x completely. Someone…
Ognjen Ognjanovic
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Cannot solve quadratic equation through product sum product when the the first product is fraction

I have the folowing equation $$\frac{16}{3}x^2 - 2x -45 = 0$$ I am trying to solve it for about 40 minutes. I am starting to think I did something wrong. Maybe the equation insn't right, I derived it. I got as far as this (16/3)x2 - 2x -45 = 0 (-45…
Diego Alves
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Finding a non-linear equation from a set of points

I'm trying to figure this out and I need help. I have a set of points and I know they are quadratic because the differences between the y points aren't the same. But how do I find the equation of a nonlinear equation? X | Y -2 | -1 -1 | -4 3 | …
dev4life
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