Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

zatajuxoqj 2022-03-22

Let p(x) be a quadratic polynomial such that distinct reals a and b ,. $p (a) = a$ and $p (b) = b$ then find the roots of. $p [p (x)] - x = 0$
Well a and b are surely two of the roots which I found easily but I cannot find the other. I used the approach that $P (x) = A (x - a) (x - b) + x$ then I found $p [p (x)] - x$ from which I can easily see that a and b are it's roots but how can I find the other two.

kembdumatxf 2022-03-22

Given $3 \sqrt{- 2 (x + 3)} - 1 = | x + 3 | + a$ has exactly two real roots, then the maximum possible value of |[a]| is? ( where [] denotes the greatest integer function )

Pasegeabe85xy 2022-03-21

Solve the inequality: $\frac{a (1 - a)}{n} < \frac{1}{10^{3}}$ for $a \in R$ .

Reuben Brennan 2022-03-21

Solve the equation $z^{3} - 2 z^{2} + 3 z - 2 = 0 .$
If a is a complex solution of this equation, what does A equal?
$A = \frac{{| a |}^{2}}{1 - i^{43}}$

meli199939f 2022-03-21

Solve $x^{T} A x = k$ with $k = c t e$ ?

ropowiec2gkc 2022-03-21

Solve $\tan^{2} (x) - (1 + \sqrt{3}) \tan (x) + \sqrt{3} < 0$
But I get $D = 4 - 2 \sqrt{3}$ and I don't think that's the right way to go about this.

Kiara Haas 2022-03-21

Linear matrix inequality given the bounds
If $A ≻ e q A_{min} ≻ 0, B ≻ e q B_{min} ≻ 0$ , will the following be true?
$A B A^{⊤} ≻ e q A B_{min} A^{⊤}$
How can I prove it?

Dominique Pace 2022-03-21

Let x be an integer and let d be a factor of $2 x^{2} - 1$ . Prove that $d^{2} \equiv 1 b mod 16$

Nathen Peterson 2022-03-21

Let x and y be two real positive integers, such that: $x + y + x y = 3$ prove that $x + y \geq 2$ .

Lorelei Stanton 2022-03-21

Let $x^{2} - (m - 3) x + m = 0, (m \in R)$ a quadratic equation. Find the value of m for which at least one root is greater than 2

mwombenizhjb 2022-03-21

Let $f (x) = x^{2} + a x + c$ where a,c are real numbers. Prove that there exist quadratic polynomials p(x) and q(x) (with real coefficients) having all roots real such that $f (x) = d \frac{1}{2} [p (x) + q (x)] .$

Samara Richard 2022-03-21

Let $f (x) = {x^{2} + 10 x + 20}$ then the number of real solutions of $f (f (f (f (x)))) = 0$ .

Nathen Peterson 2022-03-21

Let $f (x) = x^{2} + a x + b, a, b \in R$ . If $f (1) + f (2) + f (3) = 0$ , then the nature of the roots of the equation $f (x) = 0$ is
A) real
B) imaginary
C) real and distinct
D) equal roots

Lesnaoq73 2022-03-21

Let $α, β$ be the roots of $a x^{2} + b x + c = 0$ , where $1 < α < β$
Then $lim lim i t s_{x \to x_{0}} \frac{| a x^{2} + b x + c |}{a x^{2} + b x + c} = 1$ then which of the following statements is incorrect
a) $a > 0$ and $x_{0} < 1$
b) $a > 0$ and $x_{0} < β$
c) $a < 0$ and $α < x_{0} < β$
d) $a < 0$ and $x_{0} < 1$

Pasegeabe85xy 2022-03-21

Let $a \in R$ . The number of distinct solutions (x, y) that satisfy the system of equations ${(x - a)}^{2} + y^{2} = 1$ and $x^{2} = y^{2}$ can only be ?.

Alexis Alexander 2022-03-20

Solve the equation:
$\frac{1}{x^{2}} = (- 5 + \sqrt{3})$

Jasper Dougherty 2022-03-20

Solve the equation $11^{2 {(\log_{5} (x))}^{2}} - 12 \cdot 11^{{(\log_{5} (x))}^{2}} + 11 = 0$

basura8w081 2022-03-20

Solve $x^{2} + 3 x + 17 \equiv 0 (\mod 315)$

Alisa Duarte 2022-03-19

Can this be an onto function?
A function $f : R \to R$ , where R is set of real numbers, is defined by
$f (x) = \frac{α x^{2} + 6 x - 8}{α + 6 x - 8 x^{2}}$
Find the interval of values of α for which f is onto. Justify your answer.

maxime99bl6 2022-03-18

Algebraic and Trigonometric expression is $> 0$ for all real x
$2 x^{2} \sin x + 2 x \cos x + 2 x^{2} + 1$

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Algebra I

Quadratic Function Real Life Examples and Applications