Questions on quadratic equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-h)^2+k$ or $y=a(bx+c)(cx+d)$.

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6
votes
1answer
60 views

Coincidence? : $d(ax^2+bx+c)/dx=\pm \sqrt{\Delta}$

As the title says, is it just a coincidence that $d(ax^2+bx+c)/dx=\pm \sqrt{\Delta}$? (where $\Delta=b^2-4ac$, i.e. discriminant of the quadratic). We can get this easily from rearranging the ...
-1
votes
2answers
56 views

Using the quadratic equation to find the time for the ball to drop to a fifth of the height of the building

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. The distance travelled before it reached the ground is as follows... $$s = U_0 t + ...
-2
votes
1answer
12 views

parabolic function, sth deal with period [on hold]

the room temperature can be described by$T=-\frac{5}{24}(t-12)^2 +38$, where $T$ is the temperature in degrees and $t$ is the number of hours from $00:00$am. Find that the temperature is above $28$ ...
0
votes
0answers
7 views

parabolic function

The main structure of the Hale Street Bridge, being constructed across the Brisbane river, is a parabolic arched bridge with a span of 60 meters. The maximum height of the arch above water level must ...
0
votes
0answers
47 views

A question using quadratic equations. [duplicate]

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. the distance travelled before it reached the ground is as follows... s = Uot + 1/5gt2 where Uo ...
2
votes
1answer
26 views

is the sum of roots of a quadratic with rational coefficients always rational

quadratic is $ax^2 + bx +c = 0$ let the roots be $f$ and $g$ as $f + g = -\frac{b}{a}\ $ and $\ f \cdot g = \frac{c}{a}$ does this imply if a quadratic has rational coefficients the sum of the ...
0
votes
1answer
18 views

Can you simplify a coordinate

Can you simplify $(-6,-36)$ to $(-1,-6)$ if the first coordinate is the min value of a quadratic graph. The equation is $y = x^2 + 12x$.
0
votes
1answer
21 views

Quadratic problem

NASA launches a rocket at $t = 0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t) = -4.9t^2 + 37 t + 101$. Assuming that the rocket will splash down into the ...
-6
votes
3answers
45 views

How to sketch the graph of the quadratic function without using a graphing utility? [on hold]

$g(x) = x^2-8$ $f(x) = 1-x^2$ $h(x) = 12-x^2$ $f(x) = x^2+7$ $f(x) = (x-6)^2+8$ $f(x) = (x+4)^2-3$ $g(x) = x^2+2x+1$ $h(x) = x^2-8x+16$
0
votes
1answer
27 views

Solving an equation involving factorial notation

I was given this problem in the text book: $$\frac{(n+4)!}{(n+2)!} = 6$$ $$n \in I $$ Since the textbook doesn't have the solution, I'm wondering if I'm right: $$\frac{(n+4)!}{(n+2)!} \Rightarrow ...
1
vote
1answer
23 views

Sum of $n^{\text{th}}$ powers of roots of quadratic

How would I go about finding an expression (preferably closed form) for the sum of $\alpha^n+\beta^n$ in terms of $\alpha + \beta$ and $\alpha\beta$ (where $\alpha$ and $\beta$ are the roots of a ...
3
votes
7answers
2k views

The perimeter of the rectangle is $20$, diagonal is $8$ and side is $x$. Show that $x^2-10x+18=0$

My friends recently took a Maths GCSE. In the paper, they came across a very difficult question which we spent a full half-hour train journey trying to figure out. We didn't manage it, so I've come ...
0
votes
1answer
15 views

Quadratic function model [closed]

Use a quadratic function to solve the problem: Two Numbers have a sum of 29 and a product that is a maximum. Determine the two numbers and the maximum product. I'd like someone to show me how to ...
1
vote
1answer
21 views

Quadratic Functions Word Problem

A holding pen is being built alongside a long building. The pen requires only three fenced sides, with the building forming the fourth side. There is enough material for 90m of fencing. Predict what ...
0
votes
1answer
31 views

solve an quadratic equation

I was reading a document , where I stucked in figuring out this equation. $f(k)= k^2-nk+\frac{n^2 - n}{2}$. This is a quadratic function of $k$. It is minimized when $k=\frac{n}{2}$ (the $k$ ...
2
votes
2answers
79 views

Find the value of $f(x)$ for $x = 2 + 2^{2/3} + 2^{1/3}$

If $x = 2 + 2^{2/3} + 2^{1/3}$, then find the value of $f(x)=x^3 - 6x^2 + 6x$. I am unable to get to the answer - end up with more than one term. Please help me solve this!
-1
votes
1answer
78 views

Quadratics Challenge [closed]

my teacher gave me this as homework. Im in the advanced math class for grade 10 and this is the A grade question. If anyone can do this with the working out and an explanation that'd be great. ...
1
vote
1answer
30 views

For the given quadratic equation find the value of p

For the equation 3x^2 + px + 3 = 0 , p>0, if one of the roots is square of the other, then p is equal to? Solving the equation, i get the value of p as -6 but the question states that p>0. Is there ...
0
votes
2answers
14 views

Quadratic Function: X intercepts.

A quadratic function with a y-intercept of 0 and an axis of symmetry of x=-1. Apparently, there is suppose to be 2 x-intercepts, which I really don't understand. How can the parabola cross the x ...
0
votes
2answers
23 views

Quadratic Functions word problem.

I have the quadratic function $$y=\frac{1}{294}(x-84)^2-24$$ that represents the shape of the cables of a certain bridge. I am suppose to be determining the vertical height of the cables above the ...
0
votes
2answers
28 views

Quadratic Functions Problem

Question: The main section of a certain bridge has cables in the shape of a parabola. Suppose that the points on the tops of the towers where the cables are attached are 168m apart and 24 vertically ...
2
votes
1answer
18 views

What is the spherical parametrization of an ellipsoid NOT centered in the origin?

I would like to know how to parametrize an ellipsoid not centered in the origin, but with its axes parallel to the main axes of the reference system. The result I am looking for would be an ...
1
vote
5answers
57 views

For what real number $c$, this equation has exactly three solutions?

For what real number c does the equation $|x^2 + 12x + 34| = c$ has exactly three solutions?
-2
votes
0answers
39 views

Using quadratic equations for problem solving [closed]

The numerator of a fraction is 3 less than the denominator. If the numerator is increased by 6 and the denominator is increased by 5, the fraction is doubled in value. Find the original fraction. At ...
0
votes
3answers
19 views

Finding dimensions using quadratic formula

A 52 m long fence is constructed on three sides of a housing block with area 240 m^2. The fourth side facing the road is left open. Find the dimensions of the block. Also here's another question I ...
10
votes
6answers
1k views

what would be the way to solve a system of equations like this one?

Solve: $xy=-30$ $x+y=13$ {15, -2} is a particular solution, but, how would I know if is the only solution, or what would be the way to solve this without "guessing" ?
1
vote
1answer
29 views

Quadratics: Solve for B and C.

If I know that the points (-1,6) and (2,3) are on the graph of the quadratic function f(x) = 2x^2 + bx + c, how do I determine b and c? Thanks to anyone who helps.
0
votes
1answer
19 views

Quadratic Functions: Determine the value of b

I'm having trouble with this question and I'm not sure what to do. Would appreciate any one who helps me out. Question: The point $(-2,1)$ is on the graph of the quadratic function: $f(x) = -x^2 + bx ...
1
vote
2answers
44 views

Quadratic Formula for complex variable with real coefficients

I have been upto proving the following $$(\forall x\in \mathbb C, ax^2 + b x + c = 0) \land(a\neq0)\Leftrightarrow (x = {\frac {-b \pm \sqrt{b^{2}-4ac}} {2a}})$$ Due to equality we need to proof bi ...
0
votes
0answers
16 views

Need to solve two equations simultaneously to get a quadratic.

$(1)$ $p=c=4-\frac{2x}{p}$ $(2)$ $c=p=\frac{2x}{c}-4$ I want to plug $1$ into $2$ and $2$ into $1$ I need to get two answers to put into quadratic form. Could you also help me with the working ...
0
votes
2answers
41 views

Consider a quadratic equation

$x^2-2(a+1)x+3a+2=0$ Where a is any real number. Find all values of a so that the equation has two distinct real roots. I tried solving for a by using the inequality $b^2-4ac\gt0$... but when i ...
0
votes
2answers
43 views

Equation with the discriminant

I'm stuck on my maths homework, and would appreciate help. The question is: Show that if the equation $(m + n)x^2 - 2mnx - (m-n) = 0$ has equal roots, then $$m^2 = \frac{n^2}{1-n^2}$$ I've worked ...
1
vote
1answer
39 views

What is the relationship between three points on a quadratic curve and the curves coefficients?

In other words, is there a formula to get the coefficients a,b and c in terms of three points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3, y_3)$? I am asking this because I have a linear algebra problem that ...
0
votes
0answers
11 views

Question on simple quadratic word problem regarding weekly revenue when price of merchandise is lowered

A store owner sells headphones at 24 dollars a piece with roughly 1000 sold per week. The store owner finds that for every 1 dollar decrease on the price per headphone he sells 100 more headphones per ...
0
votes
2answers
40 views

Can one solve this system of qudratic equations unambigiously?

Given the parameters $p_1, p_2, p_3$ I want to know if the following system can be solved: $p_1 a + p_2 c + ef = 0\\ p_1 b + cd + p_3 f = 0\\ ab + p_2 d + p_3 f = 0\\ p_1^2 +a^2+b^2=1\\ ...
2
votes
2answers
74 views

If the equation $|x^2+bx+c|=k$ has four real roots …

If the equation $|x^2+bx+c|=k$ has four real roots then which of the following option is correct : (a) $b^2-4c >0$ and $0<k<\frac{4c-b^2}{4}$ (b) $b^2-4c <0$ and ...
0
votes
3answers
31 views

Tangent of a rational function

I'm wondering if someone could help me solve a little conundrum I've been having. I'm trying to find the equation of a line with slope $-1$ tangent to the curve of a rational function. The function is ...
13
votes
10answers
4k views

Taking Calculus in a few days and I still don't know how to factorize quadratics

Taking Calculus in a few days and I still don't know how to factorize quadratics with a coefficient in front of the 'x' term. I just don't understand any explanation. My teacher gave up and said just ...
11
votes
8answers
596 views

How to factor quadratic $ax^2+bx+c$?

How do I shorten this? How do I have to think? $$ x^2 + x - 2$$ The answer is $$(x+2)(x-1)$$ I don't know how to get to the answer systematically. Could someone explain? Does anyone have a link to ...
2
votes
2answers
67 views

Quadratic Prime

We had received some questions on Quadratic equations, But I wasnt able to do one. Here it goes: Let $a,b$ be natural numbers $a>1$. Also, $p$ is a prime number. If $ax^2+bx+c=p$ for 2 distinct ...
2
votes
3answers
73 views

How do I factor this quadratic?

I'm going through the AoPS Algebra book, and I'm on the quadratics section. I'm given this challenge question: $ \displaystyle 2x^2 + 7x(\sqrt{3}) + 9 = 0$ And I have to solve for ...
1
vote
2answers
26 views

How to Find The Roots of this Quadratic Given Sum & Product

My question is: The sum of the roots of a quadratic is $55/72$, and the products of the roots is $-25/12$. Find the roots. How I'm trying to do it so far: (Also, please correct my thought process if ...
0
votes
1answer
39 views

Solve the equation $x^2+bx+c+t\log(x)=0$

There is a explicit formula to solve the equation $x^2+bx+c+t\log(x)=0$ with the constraint $x>0$?
2
votes
5answers
72 views

Algebraic process to find numbers so that $xy=45$ and $x+y=18$

Can someone help me with the following question? The sum of two numbers is $18$ and their product is $45$. Find the numbers. I know that the answer is $15$ and $3$. But how do I find that answer ...
3
votes
2answers
124 views

Convexity of Quadratic equation Inequality?

Solving an inequality of the form $x^TAx\geq0$ or $x^TAx\leq0$ is straightforward. I mean we have to check if A is positive semidefinite or negative semidefinite. But what would be the solution to the ...
2
votes
4answers
55 views

Quadratic equation - solving for x

Question: Solve the equation $$(x+2)(x+3)(x+8)(x+12) = 4x^2$$ I tried to solve the equation by expanding the LHS and then equating it to the RHS, but that just doesn't seem to be feasible. I am ...
1
vote
1answer
40 views

Quadratic equations - finding value of x

Question: Solve the equation $$\frac{2x}{3x^2 - x+2} - \frac{7x}{3x^2 + 5x+2} = 1$$ I attempted to split the two quadratic equations into their roots, however, was unable to do so. Then I tried to ...
1
vote
7answers
244 views

How to solve the quadratic equation $x^2-1=2$?

Solve $x^2-1=2$ I have no idea how to do this can somebody please help me? I have tried working it out and I could never get the answer.
0
votes
5answers
72 views

How do you factor a quadratic expression, without using the formula?

I am asked to factor $2x^2 -3x+1=0 $ using factorization, but I run into fractions, and it becomes very messy and complicated to deal with, especially since specifically asked not to use the formula. ...
2
votes
2answers
31 views

Quadratic equation not equal to zero (solving a matrix with a parameter)

I came across this in my matrix module, learning about number of solutions when the matrix has parameters. $$ \left[ \begin{array}{ccc|c} 1 & ...