1
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2answers
14 views

Setup Quadratic Word Problem

I need help setting up this quadratic word problem, I have no idea where to start. Among all pairs of (real) numbers whose sum is 17, find a pair whose product is as large as possible. What is the ...
0
votes
5answers
35 views

Smallest value of function on a line

Problem : If the point $(\alpha, \beta)$ lies on the line $2x+3y=6$, the smallest value of $\alpha^2+\beta^2$ is (a) $36/13$ (b) $6\sqrt{13}/13$ (c) $6$ (d) $13$ Solution : Since ...
0
votes
1answer
31 views

Find domain of function with quadratic numerator algebraically

I'm stuck on this problem: $$f(x) = \frac{x^2 -4}{x}$$ I need to determine why this function's domain is not: $$\{x|x \neq \pm 2\}$$ All of the examples that I've seen have the quadratic in the ...
0
votes
4answers
39 views

Finding the three unknowns

Can someone show me the steps to finding the three unknowns of these two equations. $$-a-bx+cx^2 = x^2+2x+1$$ The answers are $a=\ ...\ $, $b=\ ...\ $, and $c=\ ...$ , but I can't see how they ...
1
vote
2answers
33 views

Analytical approach to a quadratics problem

I'm a bit rusty on functions and this exercise got me thinking quite a bit. The function $y=x$ is tangent to the graph of a certain $g$ function in $x=0$. Function $g$ can be defined as: ...
0
votes
2answers
15 views

Let f be a continuous function defined on [-2009,2009] such that f(x) is irrational for each $x \in [-2009,2009]$ …

Problem : Let f be a continuous function defined on [-2009,2009] such that f(x) is irrational for each $x \in [-2009,2009]$ and $f(0) =2+\sqrt{3}+\sqrt{5}$ Prove that the equation $f(2009)x^2 +2f(0)x ...
0
votes
3answers
38 views

Find the set of real numbers ($x$ not equal to zero) such that $2x + 1/x < 3$.

Pretty straightforward question, I just had a question for the conclusion. I rearranged, and factored and have the quadratic: $$2x + 1/x < 3$$ (multiply both sides by x and rearrange) $$2x^x - ...
0
votes
0answers
14 views

How to minimize this quadratic function?

As described at page 3 of this document, I need to minimize the following quadratic function: $E(w,x,y,z) = \sum_i \frac{(w-T_i(x,y,z))^2}{1+|\Delta f(x_i,y_i,z_i)|^2} $ where $w=f(x,y,z)$ and ...
0
votes
0answers
14 views

Quadratics and function question

A quadratic function is given by ${h(x) = ax^2 + bx + c}$ where ${a}$, ${b}$, and ${c}$ are all nonzero real numbers. The function ${h(x)}$ intersects the x-axis at two distinct points and satsifies ...
0
votes
1answer
19 views

What is the minimum possible $ non $ integral value of a

Let a A subscript(m) (m=1,2,3,....p) be the possible integral values of a for which the graphs of $ f(x)=ax^2+2bx+b $ and $g(x)=5x^2-3bx-a$ meets at some point for all real values of b. 1) What is ...
0
votes
1answer
44 views

Determining quadratic function of this word problem

I have this word problem in my homework: ...
0
votes
2answers
31 views

What does each term in the trinomial represent and their relation to each other? [duplicate]

I am trying to get a grasp or concept understanding what how trinomials answer questions other than answering questions in an algebra class. I. Looking for the practical application. What does the ...
1
vote
1answer
54 views

Found an example for solving via quadratic formula in a book where I am wondering if this is correct

As a refresher, I was skimming through a free Calculus online textbook "MOOCULUS massive open online calculus" (https://mooculus.osu.edu/handouts) and stumbled upon the following example solving a ...
-1
votes
1answer
48 views

Finding the rule of a quadratic graph

I am trying to find the rule. Insofar: $y = a(x-b)^2 + c$ Turning point is $ (1,9) $ So $ b = 1 $ and $ c = 9 $ $y = a(-4-1)^2 + 9$ $-16 = a(-4-1)^2 + 9 $ $-25 = a (-4-1)^2 $ $-25 = a (-5)^2 ...
0
votes
1answer
52 views

if f(x) is the polynomial (coeff of leadin term is unity) in 'x' of least degree such that f(1)=5 , f(2)=4, f(3)=3, f(4)=2, f(5)=1, then f(0)=?

If $f(x)$ is the polynomial (coefficient of leading term is unity) in 'x' of least degree such that $f(1)=5 , f(2)=4, f(3)=3, f(4)=2, f(5)=1$ Then $f(0)= ?$
1
vote
2answers
792 views

coefficients of quadratic function?

In a quadratic function: coefficient $a$ controls the speed of increase/decrease from the vertex. coefficient $b$ controls the downward slope as the function crosses the y-axis. I don't really ...
3
votes
4answers
59 views

How to search quadratic function

If a graph of the quadratic function $f(x)=ax^2+bx+c$, where $a$, $b$ and $c$ are constants. If this function vertex is $(13,−169)$ and the distance between the two intersection points with the ...
3
votes
3answers
147 views

Is it possible to find out $x^2$ parabola and function from 3 given points?

I am programming a ball falling down from a cliff and bouncing back. The physics can be ignored and I want to use a simple $y = ax^2$ parabola to draw the falling ball. I have given two points, the ...
4
votes
2answers
128 views

Finding the Extrema of a Function (without differetiation)

$$ (t^2-t+1)/(t^2+t+1) $$ prove that the function is upper bounded by 3 and lower bounded by 1/3 without differentiation
4
votes
4answers
399 views

Quadratic function concepts

My teacher was explaining quadratics in my class and it was a little bit unclear to me. The problem was Suppose $at^2 + 5t + 4 > 0$, show that $a > 25/16$ . My teacher said that there are ...
1
vote
1answer
3k views

Using translation and change of scale to sketch graphs of these quadratics

I borrowed the following problems from MIT open courseware problem sets. (This is the very first problem in the problem set.) I understand what completing the square is, but what does it mean when ...
1
vote
2answers
230 views

If a quadratic is reflected on the y axis, why does $b=0$?

If a quadratic in the form $y=ax^2+bx+c$ is reflected on the $y$ axis, why then must $b=0$, making the equation in the form of $y=ax^2+c$? I can remember the rule, but the reasoning behind it has ...