Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Rubi Reid 2022-03-12

What is the range of the function $f (x) = \frac{7 x^{2} - 4 x + 4}{x^{2} + 1}$ ?

Reilly Knox 2022-03-12

What is the vertex of
$(x^{2}) - 2 x - 2 p - (p^{2})$

Carleigh Young 2022-03-12

What should be the relationship between p and q, so that
$x^{4} + p x^{2} + q = 0$
equations has four solutions which are successive members of arithmetic equation.

2akondupa 2022-03-12

When faced with the factorization
$(α - 1 - λ) (μ - 1 - λ) = 0$
the roots of $λ$ can simply be said to be $α - 1$ and $μ - 1$ .
Why is that answer different to the following working?

DeamyKetSate1m 2022-03-12

Why is the discriminant of quadratic $f, Δ \leq 0$ , when $f (x) \geq 0 \forall x \in R$ ?

chatarazona7sq 2022-03-11

Why are the roots of $y^{2} - i y + 2 = 0$ not complex conjugates?

Tyshawn Mcdonald 2022-03-08

Zeros of polynomial
$f (z) = z^{2} + a z + p^{11}$
1) f has a zero on imaginary axis.
2) f has a zero for which real and imaginary parts are equal.
3) f has distinct roots.
4) f has exactly one root.

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?

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."

omdw1u 2022-03-04

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

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
$(\sum_{k = 1}^{n - 1} {{a_{k}}^{2}}) x^{2} + 2 (\sum_{k = 1}^{n - 1} a_{k} a_{k + 1}) x + (\sum_{k = 2}^{n} {{a_{k}}^{2}}) \leq 0$

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.

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 $\frac{(a - b) (2 a - b)}{a (a - b + c)}$

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

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.

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?

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?

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?

Finding a reliable quadratic function solver is quite popular today as students look for answers to equations that they encounter during those Algebra tasks. Still, quadratic function examples with answers are not so common, which is why we have collected related questions and answers for you to help you find various solutions and learn. Take your time to explore quadratic function questions. If you manage to understand at least one quadratic function solution, you will understand all the rest because it is exactly how things work. Even the most complex quadratic function equation makes sense when you have an example.

Algebra I

Quadratic Function Real Life Examples and Applications