Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

peggyleuwpodg 2022-03-25

Given $x^{2} - 3 x + 6 = 0$ find $x^{4}$ in terms of x.

aidinacol7 2022-03-25

Given quadratic equation:
$7 x^{2} - (k + 13) x + k^{2} - k - 2 = 0$ , where k is a constant, has two distinct real roots $α and β$ . Given that $0 < α < 1$ and $1 < β < 2$ , find the range of values of k.

Jazmyn Holden 2022-03-25

Given a quadratic equation, find a value of a such that the quadratic equation would have one root less than -1 and another greater than 1.

Leroy Davidson 2022-03-25

Given a quadratic equation, find values of a such that the equation will have four different solutions.
$2 a {(x + 1)}^{2} - | x + 1 | + 1 = 0$

Adolfo Hebert 2022-03-25

Given a complex number $ω = \cos (\frac{2 π}{5}) + i \sin (\frac{2 π}{5})$

Coradossi7xod 2022-03-24

How can we make it easy to solve quadratics without the Quadratic Formula?
For example,
$5 x^{2} - 7 x - 2 = 0$
Then, we only need to find is when
$5 x^{2} - 7 x = 2$
$x (5 x - 7) = 2$
Since that when we get $2 - 2 = 0$ .
Is there any way we can find them easily without solving quadratics using formula?

Samara Richard 2022-03-24

How can one solve this without expanding.
$\begin{array}{l} If a + b + c = 1, a b + b c + c a = 2 \end{array}$
$\begin{array}{l} and a b c = 3 . What is the value \end{array}$
$of a^{4} + b^{4} + c^{4} ?$

Pablo Dennis 2022-03-24

How can I prove that
$\sum_{i = 1}^{n} a_{n} \cdot \exp (q_{n} (x)) = 0$
cannot have more than two roots?

amonitas3zeb 2022-03-24

Given that $x^{2} + a x + b > 0$ and $x^{2} + (a + n p) x + (b + n q) > 0$ prove that $x^{2} + (a + \mp) x + (b + m q) > 0, m = \overset{―}{1, n - 1}$

ezpimpin6988ok1n 2022-03-24

Given that $α, β$ are the roots of $x^{2} + b x + c = 0$ and $γ, δ$ are the roots of $x^{2} + b_{1} x + c_{1} = 0$ such that
$γ < α < δ < β$

Petrolovujhm 2022-03-24

Given that
$a + b = c + d = 10$ and $| a - b | > | c - d |$ , show that $a b < c d$

afasiask7xg 2022-03-24

Making a Negative Number Possible to Square Root
We are able to solve $x^{2} + 4 = 0$ by square rooting both sides, but if we have $x^{2} = - 4$ we can't solve. Firstly, why? Aren't they equal expressions?
Secondly, if we have $x^{2} = - 4$ , why can't we bring the four to the other side, square root it and then bring it back?

blestimd4pz 2022-03-24

Making a Quadratic Function spit out Integer Outputs for Rational Inputs
Suppose I have a quadratic function
$f (x) = a x^{2} + b x + c, a, b, c \in ℤ$
and I want to find rational (non-integer) values of x for which $f (x) \in Z$ .

London Douglas 2022-03-24

For which a,b,c is the diophantine quadratic equation $a x^{2} + b x + c = y^{2}$ souble?

mwombenizhjb 2022-03-24

For which y is $3 x^{4} - 4 x^{2} y + y^{2} < 0$
How does one show that the function $f (x, y) = 3 x^{4} - 4 x^{2} y + y^{2}$ is negative for $x^{2} < y < 3 x^{2}$

Alfredo Holmes 2022-03-24

Local extrema of the function $f (x) = x^{3} - 3 α x^{2} + 3 (α^{2} - 1) x + 1$

siliciooy0j 2022-03-24

Line $x + k y + k^{2} = 0$ is tangent to curve $y^{2} = 4 x$ at point P. Find the coordinates of P in terms of k.

Leroy Davidson 2022-03-24

Let $x, y \in R^{n}$ . Let A be a $n \times n$ positive-definite symmetric matrix. Is there a general formula for $x^{T} A x \cdot y^{T} A y$ ?
For example, let $x = [\begin{matrix} 2 \\ 2 \end{matrix}], y = [\begin{matrix} 3 \\ 3 \end{matrix}], A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
Then $x^{T} A x \cdot y^{T} A y = 8 \cdot 18 = 144$
This is equal to $2 {(x \circ y)}^{T} A (x \circ y)$ where $(x \circ y) = [\begin{matrix} 6 \\ 6 \end{matrix}]$ is the Hadamard product of x,y.
It seems that $x^{T} A x \cdot y^{T} A y = 2 {(x \circ y)}^{T} A (x \circ y)$ also works for $x = [\begin{matrix} 5 \\ 5 \end{matrix}], y = [\begin{matrix} 7 \\ 7 \end{matrix}]$ . Is this true in the general case, and if so, how do I prove it? If not, how can I find and prove a general formula?

diartrosiwk8o 2022-03-24

Let $P (z) = a z^{2} + b z + c$ , where a,b,c are complex numbers.
1) If P(z) is real for all real z then show that a,b,c are real numbers.
2) In addition to (1) above, assume that P(z) is not real whenever z is not real. Show that $a = 0$ .

Coradossi7xod 2022-03-24

Let $x_{1}, x_{2} \in R$ be the roots of the equation $x^{2} + p x + q = 0$ . Find p and q if it is known that $x_{1} + 1 and x_{2} + 1$ are the roots of the equation $x^{2} - p^{2} x + p q = 0$ .

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.

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