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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Completing the square in a different form

Say we had the function $y = -6x^2-3$ and wanted to find the turning point, my first goal is to complete the square, but this is where it all falls apart. Of course I know you can differentiate both sides with respect to $x$ and get $y'=-12x$, which…
Nav Bhatthal
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How Can I Find A, B and C Values For Long Quadratic Equation

I've got an equation like this and I want to calculate the roots of this equation. I've tried to solve it with the quadratic equation but I'm struggling to find the quadratic formula's $a, b$, and $c$ values. $$ f(x)…
tarik0
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When does a function: $f(x)=3ax^2 + 2bx + c $ has no solution?

When does a function: $f(x)=3ax^2 + 2bx + c $ has no solution? can i say that if the discriminant $4b^2 - 12ac$ is a negative number because according to the quadratic root formula square root portion is a negative number and square root of a…
user307640
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Substituting x in a quadratic formula breaks the parabola

I have a question that asks "By substituting $x=10$ in the equation, find...". This is the formula in the question, which forms a parabola (representing the path of a ball): $$y=-0.05x^2+x+1.8$$ However, if I attempt to substitute $x=10$, as stated…
Craig
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Quadratic curve fit for 3D position and times

I have many data points $(x_1,y_1,z_1,t_1)$, $(x_2,y_2,z_2,t_2)$, $(x_3,y_3,z_3,t_3)$, $(x_4,y_4,z_4,t_4)$ and so on. $(x,y,z)$ is the position of a ball bouncing and hence it looks more like a multi dimensional quadratic equation. I would like to…
BhanuKiran
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Why is the axis of symmetry of a parabola $x=-\dfrac{b}{2a}$?

There are answers where they assume that $ y$ and the discriminant are $0$. But why is that? By finding the values through the vertex form, the value of $y$ or the discriminant isn't $0$.
user324713
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Why do coefficients of standard quadratic equation affect the shape of quadratic graph?

The standard equation is ax^2 + bx + c. While I was plotting the graph on Desmos, an increase in the value of 'a' would cause the graph to be narrow, and a decrease would cause it to be broad. As for 'b', it would cause the graph to shift…
user324713
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Quadratic equation not adding up when I equate $x$

I used Mathway to find x in the equation $-1.9497137966666855 * x^2 + 0.0 * x - 1 = -0.6556211074636167 * x^2 + 0.0*x - 5$ it gave the answer $1.75811509$ and $-1.75811509$ but when I replace one of these values with $x$, for example if I plug $x =…
Jaisal Francis
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Substituting in variable at earlier stage in equation

I have a somewhat very basic question. I have the following equations. Eq1 is the first raw form and then further simplying it leads to Eq2 My question is. If I substitute k=0 in Eq1, I get 0 = -1 If I substiute k=0 in Eq2, I am able to solve the…
AlfroJang80
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What is a condition for which a quadratic expression $ax^2+bx+c$ is greater than or equal to zero?

What is a condition for which a quadratic expression $ax^2+bx+c$ is greater than or equal to zero? We know that the leading coefficient $a$ is positive for this case, but I'm confused on whether the discriminant $D$ is: $D \leqslant 0,\;\;$ or $D…
Chemistry Is My Life
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Is always the value of numerator is zero in two equal fractions with same numerator but different denominator?

$Q1$: $\frac{2x-7}{x^2-7x+12} = \frac{2x-7}{x^2-7x+10}$ I was taught that when the values of the fractions of two sides are equal and when numerator of the two sides are equal, but denominators are unequal, then the value of the numerator is…
Russell
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How much information can be gleaned from a quadratic equation?

I actually came across the question below while studying a book: A particle moves along a line so that its velocity at time $t$ is $v(t) = t^2 - t - 6$ (measured in meters per second). (a) Find the displacement of the particle during the time period…
octopus
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sum of roots of quadratic equal to the reciprocals sum

If the sum of the roots of the quadratic equation $ax^2 +bx +c+0$ is equal to sum of the squares of the reciprocals then $b^2 /ac +bc/a^2$ is equal to? What I tried I equated the sum of the roots and the sum of their reciprocals after which i got a…
Rishav Bhagat
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Don't understand the step in Deriving quadratic equation

It's from the book essenstial mathematics for computer graphics fast. I don't understand why after factorize the left side will become step 4. Can anyone explain? Thanks.
Antony Ng
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Whats going on in this quadratic?

The Question If the equation $sin^2x -k\space sinx -3 =0$ has exactly two distinct real roots in $[0,\pi]$, then find the values of $k$. The Answer Let $f(t)=t^2 -kt -3$, where $t=sinx$. Since equation has exactly two distinct real roots in…
Anili
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