Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Landen Barber 2022-03-27

Given that $2 x^{2} - 4 x y + 6 y^{2} = 9$ , find the biggest and lowest value of $2 x - y$

atenienseec1p 2022-03-27

Given that $y = 3 x^{3} + 7 x^{2} - 48 x + 49$ and that y has the same remainder when it is divided by $x + k$ or $x - k$ , find the possible values of k.

Makayla Stevens 2022-03-26

Determine the sign of
$169 \times 7 - 49 \sqrt{123}$

Addison Fuller 2022-03-26

Constraints on $x^{2} + b x + c = 0$ such that at least one root has a positive real part.

anadyrskia0g5 2022-03-26

Consider the example:
$\frac{7}{x} = 0$
If we multiply both sides by x we get
$7 = 0$
which obviously is wrong.
However with the equation
$\frac{7 x^{2} - 67 x + 126}{x (x - 2) (x - 3)} = 0$
You can multiply by zero and get
$7 x^{2} - 67 x + 126 = 0$
I think it is because there are still x's remaining in the expression. However what is the exact rule when it is allowed to multiply by zero and when it is not...

Asher Olsen 2022-03-26

Consider a quadratic equation
$x^{2} + 2 x = k + \int_{0}^{1} | t + k | d t$
Then choose the correct option(s),
A) Roots are Real
B) Roots are Imaginary
C) Roots are Distinct
D) Roots are complex number

Lucian Ayers 2022-03-26

Consider the equation ${(\log_{2} x)}^{2} - 4 \log_{2} x - (m^{2} + 2 m + 13) = 0$ . Let the real roots of the equation be $x_{1}, x_{2}$ such that $x_{1} < x_{2}$ . Find the sum of maximum value of $x_{1}$ and minimum value of $x_{2}$ .

afasiask7xg 2022-03-26

How do i approach ahead in this question
Let $a$ , $b \in N$ , a is not equal to b and the quadratic equations $(a - 1) x^{2} - (a^{2} + 2) x + a^{2} + 2 a = 0 and (b - 1) x^{2} - (b^{2} + 2) x + b^{2} + 2 b = 0$ have a common root, then the value of $\frac{a b}{5}$ is

cleffavw8 2022-03-26

How can we prove there are infinitely many solutions to $\frac{1}{x^{2} - 2 x + 3} = y$ by only staying at Further maths at High School level? Will the graph ever go below the x-axis or will stay on it?

afasiask7xg 2022-03-26

How can I solve a multivariable equation using the matrix form?
$f (x, y) = x^{2} + c y^{2} + 2 x y$
I want to find the values of c for the function f(x,y) has a minimum. However I have to solve it by writing the function in the following form:
$f (x, y) = {[\begin{matrix} x \\ y \end{matrix}]}^{T} A [\begin{matrix} x \\ y \end{matrix}]$

Alexis Alexander 2022-03-26

How can I prove that all quadratic equations are not injective?
I was trying to prove that any quadratic formula ( $a x^{2} + b x + c$ ) will not be injective, but I have a little problem.
I started by assuming $f (x) = f (y)$ . We can put x and y into the general form of quadratic function, and we get
$a x^{2} + b x + c = a y^{2} + b y + c$
Subtract c from both sides and organise a little bit and you get
$a (x^{2} - y^{2}) + b (x - y) = 0$
$a (x + y) (x - y) + b (x - y) = 0$
Here we can assume that $x \neq y$ , hence $x - y \neq 0$ , so divide both sides by x-y, and we get
$a (x + y) + b = 0$
However, from here I couldn't find any contradictions, which is a problem because there must be a contradiction as quadratic functions are not injective.

anadyrskia0g5 2022-03-26

Help with solution to 2 variable quadratic equation.
Could someone help with an explanation on how to treat the equation below, please? A solution I have read uses the discriminant to find the range i.e.
$9 - 20 y^{2} - 16 y > or = 0$ . To me this means treating the variable Y as a constant , is that "acceptable" ? does anyone have a reference for these equations ?
$y x^{2} + 5 y - 3 x + 4 = 0$
rewrite as $y x^{2} - 3 x + (5 y + 4) = 0$

Jackson Floyd 2022-03-26

Given:
$a x^{2} + b x + c = 0$ with two real roots, $x_{1} > x_{2}$ , find a quadratic equation whose roots are $x_{1} + 1 and x_{2} - 1$ without solving the first equation

rijstmeel7d4t 2022-03-25

Determining how the given number lies in relation to the roots of a quadratic equation
Say we have a quadratic $x^{2} + p x + q = 0$
If this quadratic has 2 roots, then:
For any number, $λ$ , if $λ^{2} + p λ + q < 0$ then $λ$ lies between both roots.
and for any number $λ$ , if $λ^{2} + p λ + q > 0$ then if $2 λ + p > 0$ , then $λ <$ either of the roots.
1) I don't understand graphical (physical) meaning - What is $(2 λ + p)$ and what is $2 λ + p < 0 and 2 λ + p > 0$
2) Also, what is $λ^{2} + p λ + q > 0$ and $λ^{2} + p λ + q < 0$ .

Sanai Huerta 2022-03-25

Derivation for finding vertex and turning point of parabola?
Form the equation of parabola.
$y + \frac{D}{4 a} = a {(x + \frac{b}{2 a})}^{2}$
So , to find vertex of turning point ,
Make $y = 0 and x = 0$ .
You get $- \frac{b}{2 a}$ and $- \frac{D}{4 a}$ but aren’t we getting these values in +?

Guadalupe Glass 2022-03-25

How do I compute the minimum or maximum LINE of a bivariate quadratic function?
$y = g (x, w) = a x^{2} + b x w + c w^{2} + d x + e w + f$

Javion Kerr 2022-03-25

How could I find x in this equation
$x^{2} - x + 6 \equiv 0 (\mod 9)$

Leroy Davidson 2022-03-25

How can you deduce a cubic polynomial given two quadratic divisors, their respective remainders, and nothing else?
A cubic polynomial gives the remainders $(5 x + 4)$ and $(12 x - 1)$ when divided by $(x^{2} - x + 2)$ and $(x^{2} + x - 1)$ respectively.
How can I find the polynomial from this set of information?

Amya Horn 2022-03-25

Given the following quadratic equation:
$f (x) = x^{2} - 3 x - 1$
For $x, 1 \leq x \leq 100, x \equiv 1 mod 2$
Is this true for all $x \in ℤ$ ? If so, is there a way to prove it?

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