Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

basura8w081 2022-04-01

Range of p satisfying quadratic inequality
What is the set of values of p for which $p (x^{2} + 2) < 2 x^{2} + 6 x + 1$ , for all real values of x?

Reuben Brennan 2022-04-01

Range of an expression related to coefficients of a quadratic equation
Let $a x^{2} + b x + c = 0$ be a quadratic equation such that both the roots lie in [0,1]. What is the range of the expression $\frac{(a - b) (2 a - b)}{a (a - b + c)}$ ?

rijstmeel7d4t 2022-04-01

Question about the square root of a non-negative quadratic function.
For which values of x does this apply
$\sqrt{x^{2} + 2 x + 1} = x + 1$

zatajuxoqj 2022-04-01

$x^{2} + 2 a x + b = 0$ where $x_{1}$ and $x_{2}$ are real solutions.
For which value of b function $f (b) = | x_{1} - x_{2} |$ reaches maximum if $| x_{1} - x_{2} | = 2 m$

tf906571 2022-03-31

Which function best models the data?

London Douglas 2022-03-31

The equation $\sin^{4} x - (k + 2) \sin^{2} x - (k + 3) = 0$ possesses a solution if:
A) $k ≻ 3$
B) $k < - 2$
C) $- 3 \leq k \leq - 2$
D) k is any (+ve) value

swtda03u7bo 2022-03-31

Suppose $x_{1}, x_{2}$ are roots of the equation $x = 5 - x^{2}$ . Find the equation with roots $\frac{1}{{(x_{1} + 1)}^{3}} and \frac{1}{{(x_{2} + 1)}^{3}}$ .
1) $125 x^{2} + 16 x = 1$
2) $125 x^{2} = 16 x + 1$
3) $125 x^{2} = 12 x + 1$
4) $125 x^{2} + 12 x = 1$

michiiiiiakqm 2022-03-31

Suppose $x^{1}$ and $x^{2}$ are solutions to $x^{2} + x + k = 0$ , if $x_{{1}}^{2} + x_{1} x_{2} + x_{2}^{2} = 2 k^{2}$ , find the value of k.

Nadia Clayton 2022-03-31

I have a question where it is asking to find the values of a for which the graph of $f (x) = x^{2} + 2 x + a$ will intersect with its inverse. I solved it to the point where $a = - x (x - 3)$ , but how do you solve for a?

navantegipowh 2022-03-31

I have a quadratic equation, $b x^{2} + 2 a x + b = 0$ , with $a > b > 0$ . I can solve this as followings,
$x_{+} = \frac{- a + \sqrt{a^{2} - b^{2}}}{b}, x_{-} = \frac{- a - \sqrt{a^{2} - b^{2}}}{b},$
In my text book, an inequality equation, $x_{{+}}^{2} < 1 < x_{{-}}^{2}$ , is written with the solution, but I cannot derive the equation. If you can, please teach me the derivation.

Sage Fry 2022-03-31

Solving the quadratic equation $a X^{2} + a Y^{2} + 2 b X + 2 c Y + d = 0$

Dominique Pace 2022-03-31

Solving $x^{2} - ⌊ x ⌋ - 4 = 0$

navantegipowh 2022-03-31

I am having a difficult time understanding what I am doing wrong with quadratics.
$5 x^{2} - 15 x - 4 = 0$

Pizzadililehz 2022-03-31

Solving $2 + \frac{1}{\cos^{2} x} + \frac{5}{\cos x} = 0$

talpajocotefnf3 2022-03-31

How to think while solving question like this? If $a x^{2} + b x + c = 0$ has roots A and $A^{n}$ , then ${(a c^{n})}^{\frac{1}{n + 1}} + {(a^{n} c)}^{\frac{1}{n + 1}} + b = 0$

dotzis16xd 2022-03-31

Solving $\frac{x^{2} + 12 x + 4}{x + 2} = 6 \sqrt{x}$

ICESSRAIPCELOtblt 2022-03-31

How to solve this quadratic equation (with x represented by a fraction containing a square root)?
If $x - \frac{4}{5} = \pm \frac{\sqrt{31}}{5}$ , how can I find the values of a and b in the following equation?
$5 x^{2} + a x + b = 0 ?$
I've tried substituting $(\frac{4}{5} \pm \frac{\sqrt{31}}{5})$ for x and got totally confused there.

aanvarendbq28 2022-03-31

Solving for y, given
$x = \frac{- 1 + \sqrt{1 + (4 \frac{y}{50})}}{2}$

diartrosiwk8o 2022-03-31

$2 a^{2} - b c - 9 a + 10 = 0$ then the range of ‘a' is?
Let a, b and c be real numbers such that $2 a^{2} - b c - 9 a + 10 = 0$ and $4 b^{2} + c^{2} + b c - 7 a - 8 = 0$ , then the range of ‘a' is?

Caerswso1pc 2022-03-31

Solving for x in a (modified) quadratic
${(\sqrt{49 + 20 \sqrt{6}})}^{\sqrt{a \sqrt{a \sqrt{a \dots \infty}}}} + {(5 - 2 \sqrt{6})}^{x^{2} + x - 3 - \sqrt{x \sqrt{x \sqrt{x} \dots \infty}}} = 10$
where $where a = x^{2} - 3, (a \neq 0), Solve for x$

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