Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Hugh Soto 2022-04-02

Quadratic equation with one of the roots as a part of equation
If $α, β$ are roots of $x^{2} - 4 α + 1 = 0,$ then equation whose roots are $\frac{1}{4 - α}, \frac{1}{4 - β}$ is?

Caerswso1pc 2022-04-02

Prove that $\frac{π^{e}}{x - e} + \frac{e^{π}}{x - π} + \frac{π^{π} + e^{e}}{x - π - e} = 0$ has one real root in $(e, π)$ and other in $(π, π + e)$ .

Erik Cantu 2022-04-02

Proove that knowing that lines $y = a_{1} x + b_{1} x^{2} and y = a_{2} x + b_{2} x^{2}$ coincide in every point we can infer that $a_{1} = a_{2} and b_{1} = b_{2}$ .

Lesnaoq73 2022-04-02

Prove directly from the definition that
$lim : lim_{x \to - 2} x^{2} + x - 5 = - 3$

Sanai Huerta 2022-04-01

The equation $y^{2} = 4 x + 4 y$ changes to the form $y^{2} = 4 x$ if the origin shifted to (without rotating the axis)
A: (1, 2)
B: (-1, 2)
C: (-1, -2)
D: (1, -2)

nomadzkia0re 2022-04-01

The Equation $- 2 x^{2} + k x - 2 = 0$ has 2 different real solutions. Find the set of possible values of k.

Zoie Phillips 2022-04-01

Technique for solving $\frac{a x + b}{c x + d} = \frac{p x + q}{r x + s}$ where the sum of numerators equals the sum of denominators
I was looking up some shortcuts to solve quadratic equations. I got a technique that applies when the sum of the numerators and denominators are equal, but I am unable to understand the reasoning behind it. Here I'm showing an example:
$\frac{3 x + 4}{6 x + 7} = \frac{5 x + 6}{2 x + 3}$

Pablo Dennis 2022-04-01

System of two quadratics equation, P(x) and Q(x)
If $P (x) = a x^{2} + b x + c and Q (x) = - a x^{2} + d x + c, a c \neq 0$ , then the equation P(x). $Q (x) = 0$ has
(A) Exactly two real roots
(B) At least two real roots
(C) Exactly four real roots
(D) No real roots

Aryan Salinas 2022-04-01

I have to find the values of k for which the equation:
$x^{4} - (k - 3) x^{2} + k = 0$
has: (i) four real roots and (ii) exactly 2 real roots.

tibukooinm 2022-04-01

Suppose that m and n are integers, such that both the quadratic equations
$x^{2} + m x - n = 0$
and $x^{2} - m x + n = 0$
have integer roots. Prove that n is divisible by 6.

alparcero97oy 2022-04-01

Solving the system with $x^{2} - x y - 1 = 0$ and $2 x y - 4 y^{2} + 3 = 0$ .

atenienseec1p 2022-04-01

Solving the equatio
$X^{2} + (3 + i) X + 1 + i = 0$

atenienseec1p 2022-04-01

Solving $\frac{1}{x - 2} + \frac{1}{x - 1} > \frac{1}{x}$

serpebm2r 2022-04-01

How to solve this logarithmic equation with sum of exponential functions?
$2 x \geq \log_{2} (\frac{35}{3} \cdot 6^{x - 1} - 2 \cdot 9^{x - \frac{1}{2}})$

Asher Olsen 2022-04-01

How to solve this bi-quadratic example?
$5 {(\frac{x + 1}{x})}^{2} - 16 (\frac{x - 1}{x}) - 52 = 0$

Litzy Wallace 2022-04-01

Solving a trigonometric equation for purely imaginary numbers
"By constraining z to be purely imaginary, show that the equation $\cos (z) = 2$ can be represented as a standard quadratic equation. Solve this equation for z."

alparcero97oy 2022-04-01

Set $f (x) = x^{2} + a x + b$ .
Prove $max {| f (- 1) |, | f (0) |, | f (1) |} \geq \frac{1}{2}$

Deegan Chase 2022-04-01

Roots of a quadratic equation.
Given: $a {(f (x))}^{2} + b f (x) + c = 0 .$

mwombenizhjb 2022-04-01

Root of an equation
Given: ${(5 - y)}^{2} = {(1 - y)}^{2}$

parksinta8rkv 2022-04-01

Recursive equations for quadratic diophantine equations.
How do I determine the recursive equations for deriving integer solutions to quadratic Diophantine equations. Say I have a Diophantine equation. e.g.
$5 x^{2} - 3 x + 3 y^{2} + 2 y = 0$
How do I determine a recursive equation so that with one integer solution I can determine the other integer solutions.

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