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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 $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

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Condition for roots of the equation to be real.

Show that for $ 3 > y_1 >0 $ the roots of the equation $$(y_1-2)x^2-(8-2y_1)x-(8-3y_1)=0$$ are real, where $y_1$ is a constant. Due to my difficulties in doing this I would be grateful for your help.
Sophia Granger
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Quadratic equation!Given that 1/3 is one of the root

$$px^2-4x+p-2=0$$ root=1/3 can anyone tell me how to do step by step im stuck in the middle $$1/p+p-10/3=0 $$ :D
user222478
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Quadratics: Word Problem (Height, Width)

We're learning about Quadratics, but I'm not exactly sure how this applies to it: $\dfrac{w + h}{w} = \dfrac{w}{h}$. If the height is 16 inches, what is its width? (Round to the nearest tenth.) Can someone help me out?
johny
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track and field word problem

Word Problem: A track and field runner saves 1 hour by covering 112 km at a rate which is 2 kmph greater than the usual rate. How many hours does he usually take to travel this distance?
Crissani Manalo
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Prove that quadratic equation is 0 for any integer $a, b, c$

Prove that there exists a number $r$ such that $ar^2 + br + c = 0$ for any given integers $a, b, c$. I'm stuck on this. Particularly, I see it problematic as $r$ can probably be an irrational or imaginary(?) number.
Secret
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Let $k$ be a real number. Prove that if the equation $|x^{2} - 3x| = x-2+k$ has two distinct roots, then either $-1 < k < 2$ or $k > 3$?

The title is the problem. The condition "has two distinct roots" is ambiguous, but I assume it to be ``having exactly two distinct roots".
Yes
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How can I find the vertex of a parabola using only $x$ intercepts.

My teacher gave me this problem where I did a long jump and recorded the distance I went. He then asked us the height. My distance was 80 inches so the x-intercepts are $0,0$ and $80,0$. My question Is how can I make a quadratic Equation using only…
ethangail
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find x again in equation

I asked a similar question but I wanted to be sure understand. I have to find $x$ in the equation $$x^2=-2x-1$$ I go to left and get $$x^2+2x+1$$ Then I use a similar trick used in similar question and I get $$(x+1)^2$$ This I am not sure, but I…
Jacob
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What is the process of expanding quadratic equation

I am currently doing a math problem: $(a-b)(a^2+ab+b^2)$ However, I am not sure how I can actually expand this problem Do I multiply $(a-b)$ with each individual item within the other bracket?
user36278
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How to form a quadratic equation with real coefficients if $x_1=4-7i$?

Why is the quadratic equation $x^2-8x+65=0$? I tried to find $p$ and $q$ to form the equation but i need $x_2$ because: $$p=-(x1+x2)$$ $$q=x_1*x_2$$ so $x2=$?
common grackle
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quadratic equation max and min problem

A transit company charges $1.25$ dollars per ride and currently averages $10,000$ riders per day. The company needs to increase revenue but found that for each $0.10$ dollars increase in fare the company would lose $500 $ riders. What should the…
sniper007
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What can the "Product of Roots" be used for in quadratic form?

If I have a linear function and some kind of quadratic in x and y ie: $x^2+xy+y^2=1$ that share two roots, then I can substitute that linear function into the quadratic expression and use the Sum of Roots formulae to find the midpoint of the…
Trogdor
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Writing a equation in vertex form with an axis of symmetry, maximum height, and a point that it crosses

Suppose a parabola has an axis of symmetry of $x = -7$, a maximum height of $4$, and passes through point $(-6, 0)$. Write the equation in vertex form. Here's what I got: $y = -(x + 7)^2 + 4$ The problem is that when I plug in $(-6, 0)$, it doesn't…
John Tran
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Quadratic expression into postfix notation

I know generally how to convert an infix expression into a postfix expression; but I came lately across this quadratic expression: $\left(4y^2 + 2x - 1\right)$ that I had to convert into postfix and it raised a couple of questions for me, namely: If…
O.A.
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Conditions on polynomials with common roots.

If one root of the equation $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ is common and $a \ne b$ then: The options are as follows: $$\begin{array}{ll} (A)\quad& a + b = 0\\ (B)& a + b = -1\\ (C)& a - b = 1\\ (D)& a + b = 1 \end{array}$$ Idk how to…
BurntPi
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