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Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have?
Discriminant = b2-4ac
0
1
2
12

Ryan Farrell 2022-03-07

Would an equation in the form $a x + b = \frac{c}{x}$ be considered quadratic?
For example is $2 x + 3 = \frac{5}{x}$ quadratic?
On the one hand it has two solutions, $x = 1 and x = - \frac{5}{2}$ which is the number of solutions we'd expect from the fundamental theorem of algebra but on the other hand any equation in the form $a x + b = \frac{c}{x}$ would be undefined at $x = 0$ and every quadratic equation I'm familiar with is continuous over all real numbers. Is being continuous over all real numbers necessary for an equation to be called quadratic?

WesDiectstemiwxg 2022-03-07

Write the quadratic equation whose roots are 6 and 1, and whose leading coefficient is 3.

fun9vk 2022-03-06

You are given a quadratic function
$f (x) = a x 2 + b x + c$
and a linear function g(x).
The two functions intersect at $x = 0$ and at also at an x with $g (x) = f (x) = 0$ and where $x < 0$ .
Which of the two could, for some values of a,b,c, be an expression for g(x):
1) $g (x) = b x + c$
2) $g (x) = a x + c$

ahiahysel 2022-03-04

"When a shoe costs $80.00, there are 300 sales. Every $5.00 increase in price will result in 10 fewer sales. Find the price that will maximize income."

Tagiuraoob 2022-03-04

A and B are sets of real numbers
$A = [y ∣ y < 4]$
$B = [y ∣ y \geq 7]$
Write $A \cap B$ and $A \cup B$ using interval notation

omdw1u 2022-03-04

A caboodle of Pell's equation in one?
Find all the pairs of positive integers (x,y) satisfying
$x^{2} + y^{2} - 5 x y + 5 = 0$

Guy Rollins 2022-03-04

A lattice point in the xy-plane is a point both of whose coordinates are integers (not necessarily positive). How many lattice points lie on the hyperbola $x^{2} - y^{2} = 17$ ?
I think the answer should be 4, because $x^{2} - y^{2} = (x + y) (x - y) = 17$ . 17 has 4 factors: 1,17, -1, and -17. But I don't know if these numbers actually work.

Gary Johnson 2022-03-04

A high school quadratic problem
"If $a_{1}, a_{2}, a_{3}, \dots$ , an are distinct non-zero numbers such that
$(\sum_{k = 1}^{n - 1} {{a_{k}}^{2}}) x^{2} + 2 (\sum_{k = 1}^{n - 1} a_{k} a_{k + 1}) x + (\sum_{k = 2}^{n} {{a_{k}}^{2}}) \leq 0$

Write an equation for a line perpendicular to y=−4x−1y=-4x-1 and passing through the point (−4,−3)(-4,-3).

Aine Sellers 2022-03-03

A chord of a parabola
If a chord, which is not a tangent, of the parabola $y^{2} = 16 x$ has the equation $2 x + y = p$ , and midpoint (h,k), then which of the following is (are) possible values of p,h and k?
$A) : p = - 2, h = 2, k = - 4$
$B) : p = - 1, h = 1, k = - 3$
$C) : p = 2, h = 3, k = - 4$
$D) : p = 5, h = 4, k = - 3$
If I do it by mid point of chord formula i.e. $S_{1} = T$ then I get C) as answer, which is actually correct.
If I use the intersecting line concept i.e. $c < \frac{a}{m}$ then I don't get any answer. Why?

Fearne Castro 2022-03-03

A little bit different quadratic Gauss sum
Could anyone give me a direction on how to demonstrate that
$\sum lim i t s_{k = 0}^{N - 1} e^{- i \frac{π}{N} {(k + C)}^{2}} = \sqrt{N} e^{- i \frac{π}{4}},$
If $N \in N$ is even, for any $C \in Z$ .
Unfortunately, the left side of the above equation cannot be exactly defined as a quadratic Gauss sum since it does not have the term 2 within the argument of e and the summation coefficient is shifted by C.

Akash Matthews 2022-03-03

A quadratic equation question
The number of positive integral values of k for which
$(16 x^{2} + 12 x + 39) + k (9 x^{2} - 2 x + 11)$
is a perfect square is:
a)two
b)zero
c) one
d) none of these

trasdulaive 2022-03-03

A quadratic $a x^{2} + b x + c$ has its roots in the interval [0,1], find the maximum value of $\frac{(a - b) (2 a - b)}{a (a - b + c)}$

Jordana Boyd 2022-03-03

1) $2 x + 4.5 (25 - x) = 25$
2) $- \frac{6}{5} y - 4 = - 22$
Solve, please

Carl Hood 2022-03-03

(a) What are the conditions on the common ratio r and initial value a, that would make the resulting geometric sequence increasing?
(b) What are the conditions on the common ratio r and initial value a, that would make the resulting geometric sequence decreasing?
(c) What are the conditions on the common difference d and initial value a, that would make the resulting arithmetic sequence increasing?

Bobrovnik61j 2022-03-02

A company sells 4000 units each for $2. For every 5 cent increase, 40 fewer are sold. At what price should they sell if they want a revenue of $10450?

trasbocohf1 2022-03-02

A person has 20 M of fencing to build a chicken run for their chickens.The side of their barn is also a side of their chicken run. What is the largest area the chicken run can be if it must be rectangular?
How to solve this question?

facalqc4 2022-03-02

A researcher conducted a taste test with four types of mangoes. Each individual was blindfolded and given the samples to taste in random order with washout periods between them.
1) How many sequences are required for this study?
2) Give an example of the random sequences for two test subjects.
3) Give one example of a first order effect.

Carl Hood 2022-03-02

- $y = m x + b$ is a linear equation and represents a straight line. (The direction m is constant.)
- $y = x^{2} + b$ is quadratic and represents a parabola. (The direction of the tangent is not constant.)
- But $y = x^{2} = x \cdot x$ in linear form with the first x being the direction and y intercept being 0 in this case.
So you could say that indeed the direction depends upon x.
However, for $x = 1, m = 2$ and not 1 and indeed the derivative of $x^{2}$ is 2x.
Why? Where does the 2 come from?

When you are a high school student or someone already enrolled in college, even those simple research projects will include Algebra 1 equations, which means that getting some help cannot be avoided. Thankfully, you can access Algebra 1 problems and answers free of charge, which will let you see what Algebra 1 practice problems can be used for certain questions. Just remember to check calculations twice as these can easily get complex. The majority of Algebra 1 answers will be familiar to most students dealing with financial concepts as it is not related to advanced Math problems in most scenarios.

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