Quadratic Function Examples and Solutions

High School
Algebra
Algebra I
Quadratic function and equation

Recent questions in Quadratic function and equation

Essence Ingram 2022-04-05

Find the value of $f (0)$ , given $f (f (x)) = 0$ has roots as $1 & 2, f (x) = x^{2} + α x + β$

Karla Thompson 2022-04-05

Find the quadratic equation from given relatioship
The quadratic equation whose roots are a and b where
$a^{2} + b^{2} = 5 and 3 (a^{5} + b^{5}) = 11 (a^{3} + b^{3})$

Petrolovujhm 2022-04-05

Find all integers $n (n > 0)$ such that the which quadratic equation
$a_{n + 1} x^{2} - 2 x \sqrt{\sum_{k = 1}^{n + 1} a_{k}^{2}} + \sum_{k = 1}^{n} a_{k} = 0$
has real roots for every choice of real numbers $a_{1}, a_{2}, \dots, a_{n + 1}$ .

Erik Cantu 2022-04-05

Figuring out coefficients of composition of a first degree polynomial into a quadratic
Given: $g (x) = x^{2} + x - 2$ and $g \circ f = 2 [2 x^{2} - 5 x + 2]$ , find f(x)(f(x) is form $a x + b$ )

Oxinailelpels3t14 2022-04-05

f(x), g(x), 2 quadratic polynomials:
$| f (x) | \geq | g (x) | \forall x \in R$ . Find the number of distinct roots of equation $h (x) h^{″} (x) + {(h^{'} (x))}^{2} = 0$ if $h (x) = f (x) g (x)$

Aleah Choi 2022-04-05

Double root in Trigonometric equation?
Consider the function $f (x) = \sin^{2} x + \sin x$ in the domain $[0, 2 π]$ , find the subset of the domain where $f \geq 0$ .

Lorelei Stanton 2022-04-05

E.g. to find the extremum of $f (x) = x - x^{2}$ we can notice that $f (x) = 6 x - x^{2} = x (6 - x) = (6 - x) x$ . This operation maps every value x to $6 - x$ through the axis of symmetry and vice-versa (e.g. 0 is mapped to 6 and 6 mapped to 0). This operation preserves symmetry for $x = 3$ the axis of symmetry and hence the extremum of the function.
What about the function $f (x) = 6 x + x^{2} = x (6 + x) = (6 + x) x$ ? We know that the minimum of this function is at $x = - 3$ but $6 + (- 3) = 3$ . Also this operation maps e.g 4 to 10, but 10 to 16! Hence, this approach fails with this example (symmetry is not preserved).
Why is that so? Why is this approach not working for all the quadratic functions?

Javion Kerr 2022-04-05

Drawing two perpendicular tangent line from the origin to $y = x^{2} - 2 x + a$ .
We drew two perpendicular tangent line from the origin (the point (0,0) ) to the curve $y = x^{2} - 2 x + a$ , what is the value of a?
1) $\frac{5}{4}$
2) $\frac{- 5}{4}$
3) $\frac{3}{4}$
4) $\frac{- 3}{4}$

r1fa8dy5 2022-04-05

Does $\sqrt{1 + \sqrt{2}}$ belong to $Q (\sqrt{2})$ ?

Dexter Odom 2022-04-04

Find all the real roots of
$x^{2} + \frac{x^{2}}{{(x + 1)}^{2}} = 3$

Harold Hoover 2022-04-04

Find all the values of a for which both the root of the equation $(a - 2) x^{2} - 2 a x + a = 0$ lies in the interval $(- 2, 1)$ ,

Janiyah Hays 2022-04-04

Find all integer values of m such that the equation $\sqrt{9 - x} = \sqrt{3 m - x^{2} + 9 x} - \sqrt{x}$ has exactly four distinct real roots.

Lorelei Stanton 2022-04-04

Factoring the quadratic equation $3 x^{2} - 23 x + 14 = 0$

afasiask7xg 2022-04-04

Factor a quadratic when the leading coefficient is not equal to 1 and you can't factor by grouping?
If one has a quadratic, for example $5 x^{2} - 10 x - 2$ , which has real roots which via the quadratic equation are $\frac{5 \pm \sqrt{35}}{5}$ , can you find its factored form. As I understand it $5 x^{2} - 10 x - 2 \neq (x - root1) (x - root2)$ ? How can you turn this type of quadratic into a factored form?

hetriamhageh6k20 2022-04-04

Solve for x in the equation $(x - 4)^{2} = 100$ .

Jace Wright 2022-04-04

Solve for w: $(w - 2)^{2} = 225$ .

encaderpwp 2022-04-03

Find all real values of x which satisfy $\sqrt{x^{2} + 1} + x^{2} + 1 = 90$ .

Jasmine Todd 2022-04-03

Find all roots of the polynomial equation $p (p (x)) - x = 0$ .
Let p(x) be a quadratic polynomial such that for distinct reals $α and β$ ,
$p (α) = α & p (β) = β$
Show that $α and β$ are the roots of the following equation
$p (p (x)) - x = 0$

serpebm2r 2022-04-03

Find all $x, y, x > 0$ such that
$3 (x + \frac{1}{x}) = 4 (y + \frac{1}{y}) = 5 (z + \frac{1}{z})$
$x y + y z + z x = 1$
The only solution should be $x = \frac{1}{3}, y = \frac{1}{2}, z = 1$ . There is a way to do it with $x = \tan α$ .

Beryneingmk39 2022-04-03

Find a, b such that $x^{2} - x - 1$ is a factor of $a x^{9} + b x^{8} + 1$ .

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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